scientific article

zbMath0305.15001MaRDI QIDQ4061081

Adi Ben-Israel, Thomas N. E. Greville

Publication date: 1974

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra (15-01)

Related Items

Convergence of Newton-like methods for singular operator equations using outer inverses, Coupling operators, Wedderburn-Forney spaces, and generalized inverses, Techniques for the mathematical analysis of neural networks, Limiting behavior of weighted central paths in linear programming, Pre-test estimation in the linear regression model with competing restrictions, Sign pattern matrices and generalized inverses, Displacement structure of generalized inverse matrices, Reverse order laws for the generalized inverses of multiple matrix products, The weighted \(*\)-core-nilpotent decomposition, On the perturbation of the least squares solutions in Hilbert spaces, A multiprojection algorithm using Bregman projections in a product space, Reverse order laws for least squares \(g\)-inverses and minimum norm \(g\)-inverses of products of two matrices, The group inverse of the transformation \(\mathcal{S}(X)=AX-XB\), The perturbation theory for the Drazin inverse and its applications, On the continuity of generalized inverses of linear operators in Hilbert spaces., Parallel computation of polynomial GCD and some related parallel computations over abstract fields, Generalized and hypergeneralized projectors, On semi-star-related matrices, Equivalent conditions for generalized inverses of products, A note on nonnegative rank factorizations, Generalized inverses of random linear operators in Banach spaces, The error bound of the perturbation of the Drazin inverse, Theorems of Stein-Rosenberg type. III. The singular case, Strong underrelaxation in Kaczmarz's method for inconsistent systems, New extremal characterizations of generalized inverse of linear operators, Generalized inverses and their application to applied probability problems, Restoring rank and consistency by orthogonal projection, A theory for optimal regularization in the finite dimensional case, Some further results on matrix monotonicity, Nonnegative group inverses, Further results on the spectral decomposition of an incidence matrix, On the conditioning analysis of block approximate factorization methods, Conditioning analysis of modified block incomplete factorizations, Generalized pseudoinverses of matrix valued functions, Symmetric, positive semidefinite, and positive definite real solutions of \(AX=XA^ T\) and \(AX=YB\), The generalized Moore-Penrose inverse, A note on invariance of the eigenvalues, singular values, and norms of matrix products involving generalized inverses, A volume associated with \(m{\times}n\) matrices, Development of iterative techniques and extrapolation methods for Drazin inverse solution of consistent or inconsistent singular linear systems, Monotone iterative technique for nonlinear boundary-value problem of first-order differential systems with rectangular coefficients, An approximation theory for the estimation of parameters in degenerate Cauchy problems, Generalized inverses over Banach algebras, Covariance control with variance constraints for continuous perturbed stochastic systems, Lower eigenvalue bounds for singular pencils of matrices, Maximal elements under the three partial orders, Partial orders based on outer inverses, Conditioning of Stieltjes matrices by S/P consistently ordered approximate factorizations, Upper bound covariance control of discrete perturbed systems, Analytical bounds for block approximate factorization methods, Applications of the singular value decomposition in dynamics, Perturbation of spectral inverses applied to a boundary layer phenomenon arising in chemical networks, Relative inverses of meromorphic operator functions and associated projection functions, Solution of complex matrix equations with changing phase, Duality theory for N-th order differential operators under Stieltjes boundary conditions. II: Nonsmooth coefficients and nonsingular measures, Generalizations of matrix monotonicity, On moment-discretization and least-squares solutions of linear integral equations of the first kind, Products of EP elements in reflexive semigroups, Subproper splitting for rectangular matrices, Block generalized inverses, A note on computing the Drazin inverse, The behavior of eigenvalues and singular values under perturbations of restricted rank, Numerical solution of bifurcation problems for ordinary differential equations, Application of constrained generalized inverse to pattern classification, The method of closest approach for finding nonisolated zeros of functions, The Moore-Penrose inverses of singular M-matrices, Convergent nonnegative matrices and iterative methods for consistent linear systems, Goal programming and multiple objective optimizations. Part I, On the properties of a matrix valued derivative utilizing the Moore- Penrose inverse, A primal algorithm for interval linear-programming problems, A numerical procedure for computing the Moore-Penrose inverse, Spectral inverses and the row-space equations, Integral generalized inverses of integral matrices, A novel finite element method for two-point boundary value problems, The rank of a difference of matrices and associated generalized inverses, Splittings and iterative methods for approximate solutions to singular operator equations in Hilbert spaces, Explicit solutions to the reverse order law \((AB)^+=B^-_{mr}A^-_{lr}\), Two relations between oblique and \(\Lambda\)-orthogonal projectors, Factorization of symmetric singular M-Matrices, MP matrices, Inverses of L-fuzzy matrices, Incomplete factorizations of singular linear systems, A stationary iterative pseudoinverse algorithm, Construction and algebraic characterizations of the planar and axial transportation problems, Existence of generalized inverse of linear transformations over finite fields, Limit representations of generalized inverses and related methods, Necessary and sufficient conditions for superiority of misspecified restricted least squares regression estimator, On the product of orthogonal projectors, Partial orderings, preorderings, and the polar decomposition of matrices, On semi-orthogonality and a special class of matrices, Simultaneous polar decomposition of rectangular complex matrices, Reverse order law for reflexive generalized inverses of products of matrices, Quasidirect addition of matrices and generalized inverses, Minors of the Moore-Penrose inverse, Group inverses and Drazin inverses over Banach algebras, Generalized invertibility of Hankel and Toeplitz matrices, Elliptic matrices with zero diagonal, Group and Moore-Penrose invertibility of Bézoutians, Displacement structure of pseudoinverses, Concise row-pruning algorithm to invert a matrix, On \(l_ p\)-approximate solutions of linear equations, Symmetric singular linear control systems, Continuous pole placement for delay equations, Suboptimal Markovian smoothing estimates based on continuous curves of solutions of the algebraic Riccati inequality, Design of an adaptive missile autopilot considering the boost phase using the SDRE method and neural networks, The least squares \(g\)-inverse for the sum of multiple matrices, Operator-theoretic and regularization approaches to ill-posed problems, Output feedback adaptive robust control of hydraulic actuator with friction and model uncertainty compensation, On the convergence of power scaled Cesàro sums, Least-squares symmetric and skew-symmetric solutions of the generalized Sylvester matrix equation \(\sum_{i = 1}^s A_i X B_i + \sum_{j = 1}^t C_j Y D_j = E\), Solution to a system of real quaternion matrix equations encompassing \(\eta\)-Hermicity, The Moore-Penrose and group inverse of square matrices and the Jordan canonical form, A local characterization of observability, On \(k\)-\(EP\) matrices, A semi-iterative method for real spectrum singular linear systems with an arbitrary index, Involutions for matrices and generalized inverses, New perturbation results for equality-constrained least squares problems, Equivalence properties of the Hausman statistic based on a generalized inverse, On semigroups of normal matrices, Perturbation bounds for the generalized inverses \(A_{T,S}^{(2)}\) with application to constrained linear system., Condition number of Bott-Duffin inverse and their condition numbers, On integral representation of the generalized inverse \(A_{T,S}^{(2)}\)., Constructing fixed rank optimal estimators with method of best recurrent approximations, The Moore-Penrose inverse of a factorization, Condition number related with generalized inverse \(A_{T,S}^{(2)}\) and constrained linear systems, Accelerate overrelaxation methods for rank deficient linear systems, Oblique projectors and group involutory matrices, The representation and approximation of the \(W\)-weighted Drazin inverse of linear operators in Hilbert space., Generalized inverses and a block-rank equation., Perturbation analysis for the reduced minimum modulus of bounded linear operator in Banach spaces., Condition numbers and perturbation of the weighted Moore--Penrose inverse and weighted linear least squares problem., A splitting iterative method for \(\alpha-\beta\) generalized inverse and singular linear system., A note on the sensitivity of the solution of the weighted linear least squares problem., Condition number of Drazin inverse and their condition numbers of singular linear systems., A note on the representation and approximation of the outer inverse \(A_{T,S}^{(2)}\) of a matrix \(A\), Iterative methods for the Drazin inverse of a matrix with a complex spectrum., Decomposition of generalized polynomial symmetric matrices., Updating \(\star \)-palindromic quadratic systems with no spill-over, Variance-constrained robust estimation for discrete-time systems with communication constraints, Nonnegative matrices \(A\) with \(AA^\#\geqslant 0\)., Characterization of generalized inverses by a rank equation., New methods for computing the Drazin-inverse solution of singular linear systems, Further results on the perturbation estimations for the Drazin inverse, Robust consensus control for a class of multi-agent systems via distributed PID algorithm and weighted edge dynamics, On solutions of the matrix equations \(KX - EXF = BY\) and \(MXF^2 + DXF + KX = BY\), Solving a kind of restricted matrix equations and Cramer rule, Displacement structure of \(W\)-weighted Drazin inverse \(A_{d,W}\) and its perturbation, Condition number related with \(W\)-weighted Drazin inverse and singular linear systems, An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation \(AXB\)=\(C\), Computing Moore-Penrose inverses of Toeplitz matrices by Newton's iteration, On transformation laws for theta functions, Affine projections, An axiomatic approach to block decompositions of rings., On group inverse of singular Toeplitz matrices, Optimal recursive estimation of raw data, Computing generalized inverses of matrices by iterative methods based on splittings of matrices, Additive perturbation results for the Drazin inverse, Output feedback robust \(H \infty\) control with \(D\)-stability and variance constraints: Parametrization approach, Generalized inverses of tensors via a general product of tensors, Solution and control of PDE via global optimization methods, The geometry of basic, approximate, and minimum-norm solutions of linear equations, Block Householder transformation for parallel QR factorization, A characterization and representation of the generalized inverse \(A_{T,S}^{(2)}\) and its applications, A matrix equation from an inverse problem of vibration theory, Linear matrix equations from an inverse problem of vibration theory, Diakoptics as a general approach in engineering, The resolvent of a dilation-analytic three-particle system, Some properties of matrix partial orderings, Bézoutians of polynomial matrices and their generalized inverses, Perturbation bound of singular linear systems, Successive matrix squaring algorithm for computing the Drazin inverse, \(O(n^ 3)\) noniterative heuristic algorithm for linear programs with error-free implementation., Rank equalities for submatrices in generalized inverse \(M_{T,S}^{(2)}\) of \(M\), Displacement structure of weighted pseudoinverses, Drazin invertibility for matrices over an arbitrary ring, Tests for stability in linear structural equation systems, A weighted pseudoinverse, generalized singular values, and constrained least squares problems, Methods of computing weighted pseudoinverse matrices with singular weights, Inner inverses of Fredholm operators, The perturbation of the Drazin inverse and oblique projection, Conditioning of infinite Hankel matrices of finite rank, Moore-Penrose inverse of set inclusion matrices, Boundary value problems and related topics. Dedicated to Lloyd Jackson on the occasion of his 75th birthday, Linear Hamiltonian systems on time scales: Positivity of quadratic functionals, Some new properties of the equality constrained and weighted least squares problem, Interval mathematics, algebraic equations and optimization, Representation and approximation for the Drazin inverse \(A^{(\text{d})}\), The representation and approximation for the weighted Moore-Penrose inverse, Perturbation of least squares problem in Hilbert spaces., A new method for computing the solutions of differential equation systems using generalized inverse via Maple, The weighted Moore-Penrose inverse of modified matrices, Triple reverse-order law for weighted generalized inverses, Perturbation bound of the Drazin inverse, A characterization and determinantal formula for the generalized inverse \(A^{(2)}_{T,S}\) and its applications., Forest matrices around the Laplacian matrix, Perturbation theory for the generalized Bott-Duffin inverse and its applications, The impact of stationarity assessment on studies of volatility and value-at-risk., The reverse order law for the Drazin inverses of multiple matrix products, The stability and design of nonlinear neural networks, On \(g\)-inverses of a bordered matrix: revisited, On the convergence of iterative methods for solving singular linear systems, A no spill-over updating method for undamped structural systems, A new method for computing Moore-Penrose inverse through Gauss-Jordan elimination, The representation of the Drazin inverse of anti-triangular operator matrices based on resolvent expansions, Operators that attain reduced minimum, The iterative methods for computing the generalized inverse \(A^{(2)}_{T,S}\) of the bounded linear operator between Banach spaces, On the elastoplastic cyclic analysis of plane beam structures using a flexibility-based finite element approach, Perturbation analysis of Moore-Penrose quasi-linear projection generalized inverse of closed linear operators in Banach spaces, Nonnegativity, stability, and regularization of discrete-time descriptor systems, The optimal perturbation bounds of the Moore-Penrose inverse under the Frobenius norm, Kernels as features: on kernels, margins, and low-dimensional mappings, On the semi-continuity of generalized inverses in Banach algebras, Determination of the optimal value of relaxation parameter in symmetric SOR method for rectangular coefficient matrices, Best approximation of the identity mapping: The case of variable finite memory, Least-squares Hermitian problem of complex matrix equation \((AXB,CXD)=(E,F)\), Representation and approximate for generalized inverse \(A_{T,S}^{(2)}\): revisited, Condensed Cramer rule for solving restricted matrix equations, Interval iterative methods for computing Moore-Penrose inverse, Computational algorithms for computing the inverse of a square matrix, quasi-inverse of a non-square matrix and block matrices, Monotone maps on matrices of index one, On the \(\mathop\leq\limits^\sharp\)-order on the set of linear bounded operators in Banach space, Overdetermined linear systems satisfying nonnegativity constraints, Filtering for a class of nonlinear discrete-time stochastic systems with state delays, Dimensionality of biinfinite systems, Global optimization in \(\mathbb R^{n}\) with box constraints and applications: a MAPLE code, Further results on the reverse-order law, Semiconvergence of two-stage iterative methods for singular linear systems, Theory and practice in optimal aggregation of linear models: application of W. D. Fisher's method to input-output models, Extremal ranks of matrix expression of \(A - BXC\) with respect to Hermitian matrix, Extracting the left and right critical eigenvectors from the LDU-decomposed non-symmetric Jacobian matrix in stability problems, On Euclidean distance matrices, Generalized finite-time synchronization between coupled chaotic systems of different orders with unknown parameters, Local convergence of a secant type method for solving least squares problems, The rank reduction procedure of Egerváry, Representation of the Drazin inverse for special block matrix, Perturbation and expression for inner inverses in Banach spaces and its applications, On the idempotent solutions of a kind of operator equations, On generalized inverses and Green's relations, The common Re-nnd and Re-pd solutions to the matrix equations \(AX = C\) and \(XB = D\), Invertibility of a linear combination of two matrices and partial orderings, Smoothing factor, order of prolongation and actual multigrid convergence, A modified \(C_{p}\) statistic in a system-of-equations model, A further algebraic version of Cochran's theorem and matrix partial orderings, On stable perturbations for outer inverses of linear operators in Banach spaces, Predicting densities of nitrocubanes using partial orders, On the characteristic polynomials and eigenvalues of some specially bordered matrices, A derivative free iterative method for solving least squares problems, Load capacity ratios for structures, The additive and block decompositions about the WLSEs of parametric functions for a multiple partitioned linear regression model, Extremal ranks of some nonlinear matrix expressions with applications, Computed torque control of redundant manipulators using general-purpose software in real-time, Explicit group inverse of an innovative patterned matrix, On products of EP matrices, System identification methods for (operational) modal analysis: review and comparison, An alternative approach for generation of membership functions and fuzzy rules based on radial and cubic basis function networks, Applications of completions of operator matrices to some properties of operator products on Hilbert spaces, Eigensensitivity of symmetric damped systems with repeated eigenvalues by generalized inverse, On the estimation of sliding domains and stability regions of variable structure control systems with bounded controllers, Sliding mode observers for nonlinear models with unbounded noise and measurement uncertainties, Closed-form solutions to discrete-time LQ optimal control and disturbance attenuation, Stabilizing compensator design for uncertain nonlinear system, The geometry of the set of scaled projections, Polynomials compatible with a symmetric Loewner matrix, The composition of solutions of the multidimensional translation equation, A perturbation bound for the generalized polar decomposition, Copulas with maximum entropy, Adaptive Q-S synchronization between coupled chaotic systems with stochastic perturbation and delay, Using the GSVD and the lifting technique to find \(\{P,k+1\}\) reflexive and anti-reflexive solutions of \(AXB=C\), A comparative study of optimal linear controllers for vibration suppression, Mixed-type reverse-order laws for the generalized inverses of an operator product, Reverse order law of group inverses of products of two matrices, Rank equalities related to the generalized inverses \(A_{T,S}^{(2)}\), \(B_{T_1,S_1}^{(2)}\) of two matrices \(A\) and \(B\), Solving constrained matrix equations and Cramer rule, Necessary and sufficient conditions for the inversion of linearly-perturbed bounded linear operators on Banach space using Laurent series, A note on the group inverse of some \(2 \times 2\) block matrices over skew fields, Feasibility and solvability of Lyapunov-type linear programming over symmetric cones, Algebraic algorithms for least squares problem in quaternionic quantum theory, Representation for the \(W\)-weighted Drazin inverse of linear operators, Successive overrelaxation methods for solving the rank deficient linear least squares problem, Moore-Penrose inverse of a hollow symmetric matrix and a predistance matrix, The convergence properties for regularized Landweber method, Inverse eigenproblem for \(R\)-symmetric matrices and their approximation, Group inverse for the block matrices with an invertible subblock, The condition numbers for weighted Moore-Penrose inverse and weighted linear least squares problem, A note on the perturbation of an outer inverse, Further results on the group inverse of some anti-triangular block matrices, Block-iterative methods for consistent and inconsistent linear equations, On the matrix monotonicity of generalized inversion, Generalized inverses over integral domains. II: Group inverses and Drazin inverses, General expressions for the Moore-Penrose inverse of a 2\(\times 2\) block matrix, On the nonnegativity of \(XX^+\) and its relevance in econometrics, Chebyshev acceleration of the method of Cimmino, Matrix equations over rings, Generalized inverse method for subspace maps, Perturbation bounds for the linear least squares problem subject to linear inequality constraints, Secant relations versus positive definiteness in quasi-Newton methods, Generalizations of the spectral theorem for matrices. II. Matrix polynomials over arbitrary fields, Parameter estimation in underdetermined problems, The primal-dual algorithm as a constraint-set-manipulation device, Orthogonal considerations in the design of neural networks for function approximation., Generalized inversion of Fredholm integral operators with degenerate kernels in Banach spaces, On solutions of the matrix equations \(X\)-\(AXB\)=\(C\) and \(A{\overline{X}}B\)=\(C\), A restricted signature normal form for Hermitian matrices, quasi-spectral decompositions, and applications, Structures of \(p\)-isometric matrices and rectangular matrices with minimum \(p\)-norm condition number, The reverse order law for the generalized inverse \(A^{(2)}_{T,S}\), DFOM algorithm and error analysis for projection methods for solving singular linear system, The weighted generalized inverses of a partitioned matrix, Generalized inverse \(A^{(2)}_{T,S}\) and a rank equation, On Drazin inverse of singular Toeplitz matrix, Vector least-squares solutions for coupled singular matrix equations, Displacement structure of the generalized inverse \(A_{T,S}^{(2)}\), Drazin-Moore-Penrose invertibility in rings, Perturbation analysis of generalized inverses of linear operators in Banach spaces, On the Moore-Penrose generalized inverse matrix, On partial orderings on the set of rectangular matrices, Rank equalities related to the generalized inverse \(A^{(2)}_{T,S}\) with applications, Applications of CS decomposition in linear combinations of two orthogonal projectors, Nonlinear model-based control using second-order Volterra models, An algorithm to check the nonnegativity of singular systems, The metric generalized inverse and its single-value selection in the pricing of contingent claims in an incomplete financial market, Forward order law for \(g\)-inverses of the product of two matrices, Optimal and minimum-energy optimal tracking of discrete linear time-varying systems, Deterministic regression model and visual basic code for optimal forecasting of financial time series, The hyperpower iteration revisited, Impulsive control and optimization, The projection method for reaching consensus and the regularized power limit of a stochastic matrix, On bordering of regular matrices, On snapshot-based model reduction under compatibility conditions for a nonlinear flow problem on networks, Explicit solutions for interval semidefinite linear programs, The group inverse of a triangular matrix, On the least squares distance between affine subspaces, On inequality constrained generalized least squares selections in the general possibly singular Gauss-Markov model: A projector theoretical approach, Iterative methods for computing the generalized inverses \(A^{(2)}_{T,S}\) of a matrix \(A\), Existence of solutions to fractional boundary value problems at resonance in Hilbert spaces, On the \(\{2\}\)-inverse and some ordering properties of nonnegative definite matrices, Perturbation analysis of the least squares solution in Hilbert spaces, A self-correcting matrix iteration for the Moore-Penrose generalized inverse, Characterizations, iterative method, sign pattern and perturbation analysis for the DMP inverse with its applications, A short proof of a matrix decomposition with applications, The fundamental equations for the generalized resolvent of an elementary pencil in a unital Banach algebra, The inverse and the Moore-Penrose inverse of a \(k\)-circulant matrix with binomial coefficients, Reprint of: On generalized inverses and Green's relations, Continuous homogeneous selections of set-valued metric generalized inverses of linear operators in Banach spaces, Perturbation theory for the Fokker-Planck operator in chaos, Frames and oversampling formulas for band limited functions, Data compression under constraints of causality and variable finite memory, Discrete linear Hamiltonian eigenvalue problems, Constructing projections on sums and intersections, Convergence properties of Krylov subspace methods for singular linear systems with arbitrary index, Linear estimation in models based on a graph, Semigroups of EP linear transformations, A direct heuristic algorithm for linear programming, Representation and approximation of the outer inverse \(A_{T,S}^{(2)}\) of a matrix \(A\), Weighted Moore-Penrose inverses of arbitrary-order tensors, Jacobi fields in optimal control: Morse and Maslov indices, Monotone linear transformations on matrices over semirings, New representations of the Moore-Penrose inverse of \(2 \times 2\) block matrices, The absorption laws for the generalized inverses, Saddle point problems, Bott-Duffin inverses, abstract splines and oblique projections, Moore-Penrose inverse of the incidence matrix of a distance regular graph, Perturbations of Drazin invertible operators, Least squares Hermitian solution of the complex matrix equation \(AXB+CXD=E\) with the least norm, The Drazin inverse as a gradient, Upper and lower bounds for ranks of the matrix expression \(X-XAX\), New conditions for the convergence of Newton-like methods and applications, Some simple criteria for the solvability of block \(2 \times 2\) linear systems, Reducible solution to a quaternion tensor equation, Characterizations, approximation and perturbations of the core-EP inverse, On sums of range symmetric matrices with reference to indefinite inner product, Resistance distance of blowups of trees, Moore-Penrose inverses of the signless Laplacian and edge-Laplacian of graphs, Sharp partial order and linear autonomous systems, Characterization of optimal feedback for stochastic linear quadratic control problems, Absolutely minimum attaining closed operators, On Moore-Penrose pseudoinverse computation for stiffness matrices resulting from higher order approximation, The general solution of quaternion matrix equation having \(\eta \)-skew-Hermicity and its Cramer's rule, Core and core-EP inverses of tensors, Special least squares solutions of the reduced biquaternion matrix equation \(AX=B\) with applications, A new updating method for the damped mass-spring systems, Gauss-Seidel method with oblique direction, On the generalized Drazin-Riesz inverse for closed linear operators, Some results on the symmetric representation of the generalized Drazin inverse in a Banach algebra, Least-squares solutions of the matrix equations \(A X B + C Y D = H\) and \(A X B + C X D = H\) for symmetric arrowhead matrices and associated approximation problems, Least squares pure imaginary solution and real solution of the quaternion matrix equation \(A X B + C X D = E\) with the least norm, Closed \(EP\) and hypo-\(EP\) operators on Hilbert spaces, The best approximate solution of the inconsistent linear system via a quadratic penalty function, A criterion of solvability of resonant equations and construction of their solutions, On the existence of solutions to equality constrained least-squares problems in infinite-dimensional Hilbert spaces., Splitting based on the outer inverse of matrices., The expression of the generalized Bott-Duffin inverse and its perturbation theory, PCR algorithm for parallel computing minimum-norm \((T)\) least-squares \((S)\) solution of inconsistent linear equations, The representation and approximation for the generalized inverse \(A^{(2)}_{T,S}\), A problem in computation of pseudoinverses., On continuity of the generalized inverse \(A^{(2)}_{T,S}\), The representation and approximation for the weighted Moore-Penrose inverse in Hilbert space., Subproper and regular splittings for restricted rectangular linear system, A generalized \(\varphi\)-divergence for asymptotically multivariate normal models., Outer inverses: Jacobi type identities and nullities of submatrices, Constrained fuzzy controller design of discrete Takagi-Sugeno fuzzy models., Looking for nonnegative solutions of a Leontief dynamic model., The generalized inverse \(A_{T,*}^{(2)}\) and its applications, A relationship between the star and minus orderings, Hermitian and nonnegativity preserving subspaces, More on BLU estimation in regression models with possibly singular covariances, Matrix derivation of moving-weighted-average graduation formulas, Generalized inverses of a sum with a radical element, Generalized inverses of substochastic matrices, On matrix equations in a class of complete and completely distributive lattices, A new mixed formulation for elasticity, Generalized inverses under the \(\ell _ 1\)-norm, A note on monotonicity of a Rosenbrock method, An explicit linear solution for the quadratic dynamic programming problem, The Drazin inverse of a semilinear transformation and its matrix representation, Pták type theorem for \(C^ *\)-algebras, Generalized inverses of morphisms with kernels, The truncated SVD as a method for regularization, A finite algorithm for computing the weighted Moore-Penrose inverse \(A^ +_{MN}\), Karmarkar's projective algorithm: A null space variant for multi- commodity generalized networks, Some algebraic relations between involutions, convolutions, and correlations, with applications to holographic memories, On inertia and Schur complement in optimization, Some problems of best approximation with constraints, Nonnegative generalized inverses of powers of non-negative matrices, On inverse and generalized inverses of Hessenberg matrices, On the solution of singular linear systems of algebraic equations by semiiterative methods, Group and Moore-Penrose inverses of regular morphisms with kernel and cokernel, Polynomial acceleration of iterative schemes associated with subproper splittings, A Cramer rule for finding the solution of a class of singular equations, Coupled linear operators, Existence, uniqueness, and stability of solutions to singular linear quadratic optimal control problems, Iterative methods for solving restricted linear equations, On state restrained linear-quadratic control problems, Fehleranalyse für die Gauß-Elimination zur Berechnung der Lösung minimaler Länge, Nonnegative integral solution of linear equations, Some properties of a uniformly linearly independent sequence of subspaces, A stability theorem for systems with discrete parameters and arbitrary circulatory forces, A Drazin inverse for rectangular matrices, Nonnegative Drazin inverses, On some ordering properties of the generalized inverses of nonnegative definite matrices, The matrix equation AXB+CYD=E, Gauss and generalized inverses, On the characterization of generalized inverses by bordered matrices, On pseudoinverses of operator products, Symmetrizers of matrices, Drazin inverses and canonical forms in \(M_ 0(\)Z/h), On Lavoie's determinantal inequality, Integer generalized inverses of incidence matrices, Nonnegative integral generalized inverses, A comparison of various derivatives for matrix valued functions, A contribution to the theory of condition, Iterative algorithms for large partitioned linear systems, with applications to image reconstruction, Note on an extension of the Moore-Penrose inverse, A combined direct-iterative approach for solving large scale singular and rectangular consistent systems of linear equations, Löwner-ordering antitonicity of generalized inverses of Hermitian matrices, On g-inverses and the nonsingularity of a bordered matrix \(\begin{pmatrix} A&B\\ C&0\end{pmatrix}\), The Moore-Penrose inverse of a morphism with factorization, On the existence of bases of class \(C^ p\) of the kernel and the image of a matrix function, On inequality constrained generalized least-squares estimation, Invariance theory for infinite dimensional linear control systems, Equilibrium response of flight control systems, The product of operators with closed range and an extension of the reverse order law, The generalized Bott-Duffin inverse and its applications, Symmetric morphisms and the existence of Moore-Penrose inverses, A geometric property of the least squares solution of linear equations, Preconditionings and splittings for rectangular systems, Moving-weighted-average smoothing extended to the extremities of the data. III. Stability and optimal properties, Lattice properties of the *-order for complex matrices, On the acceleration of Kaczmarz's method for inconsistent linear systems, Kantorovich's type theorems for systems of equations with constant rank derivatives, A model updating method for undamped structural systems, A general scheme for Q-S synchronization of chaotic systems, Inverse eigenvalue problems of tridiagonal symmetric matrices and tridiagonal bisymmetric matrices, Equations \(ax = c\) and \(xb = d\) in rings and rings with involution with applications to Hilbert space operators, Comparison of bounds for V-cycle multigrid, Method of elementary transformation to compute Moore-Penrose inverse, Multicomponent transport algorithms for partially ionized mixtures, A general scheme for Q-S synchronization of chaotic systems with unknown parameters and scaling functions, Convergence behavior of Gauss-Newton's method and extensions of the Smale point estimate theory, The reverse order laws for \(\{1,2,3\}\) - and \(\{1,2,4\}\) -inverses of a two-matrix product, A review of infinite matrices and their applications, Projected iterative algorithms for complex symmetric systems arising in magnetized multicomponent transport, Towards theory of generic principal component analysis, Determinantal representation of weighted generalized inverses, Properties of unilevel block circulants, Optimal multilinear estimation of a random vector under constraints of causality and limited memory, A symmetric inverse eigenvalue problem in structural dynamic model updating, An inverse eigenvalue problem for damped gyroscopic second-order systems, Convergence of generalized inverses and spline projectors, Two-sided spectral bounds of two irreducible linear maps, A Stein-Rosenberg theorem for rectangular matrices, On the generation of updates for quasi-Newton methods, Report on test matrices for generalized inverses, EP morphisms, Generalized boundary value problems for ordinary differential operators and least squares solutions, The generalized inverse of integral matrices, Drazin-monotonicity characterizations for property-n matrices, The \(\{\) 2\(\}\)-inverse with applications in statistics, The reverse order law revisited, Maximum-likelihood estimation of the parameters of a multivariate normal distribution, Iterative methods for overflow queueing models. I, A Cramer rule for minimum-norm (T) least-squares (S) solution of inconsistent linear equations, Completing a matrix when certain entries of its inverse are specified, Nonnegative $\lambda $-Monotone Matrices, M-Matrices whose Inverses are Stochastic, On the Sensitivity of the Gravity Model, Invertibility in rings of the commutatorab – ba, whereaba=aandbab=b, Unnamed Item, The weighted Moore-Penrose generalized inverse and the force analysis of overconstrained parallel mechanisms, Estimation of the variance in any point of an electron-density map for any space group, Unnamed Item, Input optimization: I. Optimal realizations of mathematical models, Updating $LU$ Factorizations for Computing Stationary Distributions, On controlling generalized state-space (descriptor) systems, A symmetric generalized inverse eigenvalue problem in structural dynamics model updating, Additive matrix maps that are monotone with respect to the orders induced by the group inverse, Algebraic characterizations of the singular value decompositions in the transportation problem, On Symmetric and Skew-Symmetric Solutions to a Procrustes Problem, Evaluation of hypersingular integrals in the boundary element method, About the group inverse and Moore-Penrose inverse of a product, On the block independence in \(g\)-inverse and reflexive inner inverse of a partitioned matrix, Box-Jenkins identification revisited. II: Applications, State trajectories in Hilbert resolution spaces, An Application of the Moore-Penrose Inverse to Antisymmetric Relations, Solving multiple criteria problems by interactive decomposition, A note on optimal control of generalized state-space (descriptor) systems, Mean squared error matrix comparisons between biased estimators — An overview of recent results, T-Jordan canonical form and T-Drazin inverse based on the T-product, Decomposition of Nonnegative Group-Monotone Matrices, Finite transmission zeros of linear time-invariant generalized state space systems, Estimation of Sparse Jacobian Matrices, An efficient iterative updating method for hysteretic damping models, Re-nnd SOLUTIONS OF THE MATRIX EQUATION AXB=C, Adding kinematic constraints to purely differential dynamics, Output regulator problem of time-invariant discrete-time descriptor systems, Note on the weighted generalized inverse of the product of matrices, On perturbations for oblique projection generalized inverses of closed linear operators in Banach spaces, Perturbations and expressions for generalized inverses in Banach spaces and Moore-Penrose inverses in Hilbert spaces of closed linear operators, On the Drazin inverse of the linear combinations of two idempotents in a complex Banach algebra, Partial Minimax Estimation in Regression Analysis, Products of EP operators on Hilbert spaces, Inequalities in Hilbert Modules of Matrix-Valued Functions, Revisitation of the core inverse, Non-linear systems: identification and optimal control, Stabilization of polytopes of plants by their vertices, A note on the generalized rank reduction, Unnamed Item, The nearness problems for symmetric matrix with a submatrix constraint, Forward order law for the generalized inverses of multiple matrix product, On generalized inverses of singular matrix pencils, The representation and approximation for the weighted Minkowski inverse in Minkowski space, (T,S) splitting methods for computing the generalized inverse and rectangular systems^∗, On the local and global convergence of a reduced Quasi-Newton method¹, On the Matrix Equation $AX + X^ * A^ * = C$, Polynomial cost for solving IVP for high-index DAE, Analysis and design of variable structure systems using a geometric approach, Covariance control theory, Symmetric successive overrelaxation methods for rank deficient linear systems, An improved Newton iteration for the weighted Moore-Penrose inverse, L-structured matrices and linear matrix equations^∗, PCR algorithm for the parallel computation of the solution of a class of singular linear systems, A generalized finite difference method for modeling cardiac electrical activation on arbitrary, irregular computational meshes, Inverse eigenvalue problem of Hermitian generalized anti-Hamiltonian matrices, Approximate modeling of an elastic structure according to test data with various confidences, Determination of time-exponential inputs generating time-exponential state responses for linear time-invariant control systems, The use of jacobi's lemma in unimodularity theory, Group inverse for block matrix with \(t\)-potent subblock, Group inverse for a class of \(2\times 2\) anti-triangular block matrices over skew fields, Bott-Duffin inverse over the quaternion skew field with applications, Group inverse for two classes of \(2\times 2\) anti-triangular block matrices over right Ore domains, The \(\{P,Q,k+1\}\)-reflexive solution of matrix equation \(AXB=C\), Optimal dissipative control of a class of discrete-time nonlinear stochastic systems with general criteria, Local convergence theorems of Newton's method for nonlinear equations using outer or generalized inverses, On the Generalized Drazin Inverse and Generalized Resolvent, Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations, Linear matrix transformations that are monotone with respect to the \(\leq^\sharp\)-or \(\leq^{\mathrm{cn}}\)-order, Sturmian and spectral theory for discrete symplectic systems, On the Drazin inverse and M-P inverse for sum of matrices, Convergence Analysis of Newton-Like Methods for Inverse Eigenvalue Problems with Multiple Eigenvalues, Algebraic Two-Level Convergence Theory for Singular Systems, On the partitioned matrix $\begin{pmatrix}O&A\\A^\ast &Q\\ \end{pmatrix}$ and its associated system $AX=T,A^\ast Y+QX = Z$, Admissible consensus for heterogeneous descriptor multi-agent systems, Generalized mean squared error comparisons of biased regression estimators, Output function control in general state space systems containing the first derivative of the input vector, On the design of observers for generalized state space systems using singular value decomposition, Approximate and exact completion problems for Euclidean distance matrices using semidefinite programming, On transmission zeros and zero directions of multivariable time-invariant linear systems with input-derivative control, On designing reduced-order observers for linear time-invariant systems subject to unknown inputs, Gauss as Scientific Mediator Between Mathematics and Geodesy from the Past to the Present, Ill-Posed Problems: Operator Methodologies of Resolution and Regularization, Mixed-integer quadratic programming, Least-squares problem for the quaternion matrix equationAXB+CYD=Eover different constrained matrices, Semiconvergence criteria of iterations and extrapolated iterations and constructive methods of semiconvergent iteration matrices, Robust controller design for uncertain linear systems with circular pole constraints, Moore-Penrose inverse in an indefinite inner product space, The classical adjoint, Distance matrix and Laplacian of a tree with attached graphs, On the Wedderburn-Guttman theorem, On minimal-order inverses of discrete-time descriptor systems, Properties of normalr-potent matrices, On zeros of time-invariant multivariable linear systems containing input derivatives, PARALLEL CHAOTIC ALGORITHMS FOR SINGULAR LINEAR SYSTEMS, Additive results for the generalized Drazin inverse, The consistency and the general common solution to some quaternion matrix equations, \( (P,Q)-{\varepsilon} \)-pseudo condition spectrum for \(2\times 2\) matrices. Linear operator and application, Drazin inverse and generalization of core-nilpotent decomposition, Drazin-inverse and heat capacity for driven random walkers on the ring, Generalized inverses in graph theory, A coupled quaternion matrix equations with applications, GD1 inverse and 1GD inverse for bounded operators on Banach spaces, Weighted Moore-Penrose, Drazin, and group inverses of the Kronecker product \(A \otimes B\), and some applications, Projective iterative algorithms with application to multicomponent transport, A new positive definite geometric mean of two positive definite matrices, Totally isotropic subspaces, complementary subspaces, and generalized inverses, Secondary κ-range symmetric fuzzy matrices, *-DMP elements in *-semigroups and *-rings, A continuous orbit for the generalized inverse, Moore–Penrose inverse and group inverse, Construction of finite tight frames via singular value decomposition, Left and right G-outer inverses, A simplex-like method with bisection for linear programming¹, Pseudo-Similarity for Matrices Over a Field, Robust state observer design guaranteeing D-stability, Quotients of Bounded Operators, Weighted inner inverse for rectangular matrices, Strong regularity and generalized inverses in jordan systems, On the denseness of minimum attaining operators, Approximation in the identification of nonlinear degenerate distributed parameter systems, Regular factorizations and group inverses of linear operators in Banach spaces, BACKWARD PERTURBATION ANALYSIS AND RELATIVE ALGORITHMS FOR NONSYMMETRIC LINEAR SYSTEMS WITH MULTIPLE RIGHT-HAND SIDES, A cramer rule for solution of the general restricted linear equation^∗, A reduced‐order stochastic observer approach to optimal state estimation with noise‐free measurements, Numerical algorithms for solving the least squares symmetric problem of matrix equation AXB + CXD = E, Weak-Strong Uniqueness for Maxwell--Stefan Systems, Calculating the Best Approximate Solution of an Operator Equation, On an approach to the estimation of the state-variable descriptive parameters for linear continuous-time models, Restricted ridge estimator in generalized linear models: Monte Carlo simulation studies on Poisson and binomial distributed responses, Matrix mean square error comparisons based on a certain covariance structure, Controller design for continuous systems with variance and circular pole constraints, Moore-penrose involutions in the classes of laplacians and simplices, A New Semialgebraic Two-Grid Method for Oseen Problems, Spectral representation of absolutely minimum attaining unbounded normal operators, The Onsager-Machlup action functional for degenerate stochastic differential equations in a class of norms, A new image restoration model associated with special elliptic quaternionic least-squares solutions based on LabVIEW, The \(\eta\)-(anti-)Hermitian solution to a constrained Sylvester-type generalized commutative quaternion matrix equation, The absorption laws for the weighted core inverse in rings, The inverse of the incidence matrix of a unicyclic graph, The general solution to a system of linear coupled quaternion matrix equations with an application, A note on Moore–Penrose inverse of Laplacian matrix of graphs, A new partial order based on core partial order and star partial order, Algebraic techniques for the least squares problems in elliptic complex matrix theory and their applications, Generalized core-EP inverse for square matrices, Normality preserving multiplication operators, Algebraic Multigrid for Stokes Equations, An Efficient Multigrid Method for Graph Laplacian Systems II: Robust Aggregation, Moore-penrose inverse of the incidence matrix of a tree, On the uniqueness of the solution to the direct nonlinear problem of physical networks, A note on inner and reflexive inverses in semiprime rings, Representations and properties of the W-weighted core-EP inverse, On the covariance of the Moore-Penrose inverse, Characterizations of *-DMP matrices over rings, Monotone Linear Transformations on Matrices Are Invertible, Newton-Type Solvers Using Outer Inverses for Singular Equations, Vanishing pseudo–Schur complements, reverse order laws, absorption laws and inheritance properties, Pseudo core inverses in rings with involution, Approximation property of partition of unity and its applications, On k-circulant matrices with arithmetic sequence, Residual vibration suppression using Hankel iterative learning control, Some additive results on Drazin inverse, The generalized Drazin inverse of operator matrices, Recurrent neural networks for computing weighted Moore-Penrose inverse, Successive matrix squaring algorithm for parallel computing the weighted generalized inverse \(A^+_{MN}\), Operator and matrix representation for the generalized inverse \(A_{T,S}^{(2)}\), On system inversion by matrix generalized inverses, Representations for Moore-Penrose inverses in Hilbert spaces, Reduced-order filtering of jump Markov systems with noise-free measurements, Optimal observers for the state regulation of linear discrete-time plants, On input function observers for generalized state-space systems, Further results on output control in the servomechanism sense, The Moore-Penrose inverse of von Neumann regular matrices over a ring, About the von Neumann regularity of triangular block matrices, A geometrical approach on generalized inverses by Neumann-type series, DGMRES: A GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems, Group inverse and group involutory Matrices^∗, On the perturbation and subproper splittings for the generalized inverse \(A_{T,S}^{(2)}\) of rectangular matrix \(A\), Structural and computational properties of possibly singular semiseparable matrices, Transfer-function matrix synthesis by matrix generalized inverses, Second-order directional derivatives of all eigenvalues of a symmetric matrix, The group inverse of the nivellateur, A structure theorem for operators with closed range, Variable structure observer with a boundary-layer for correlated noise/disturbance models and disturbance minimization, On time optimal control of linear discrete-time systems by geometric approach, An integer arithmetic method to compute generalized matrix inverse and solve linear equations exactly, CHECKERBOARD COPULAS OF MAXIMUM ENTROPY WITH PRESCRIBED MIXED MOMENTS, Matrix Group Monotonicity, A note on the partial ordering of positive semi-definite matrices, Regular elements determined by generalized inverses, Regular morphisms in abelian categories, Some additive results on M-P inverse of operator product, Onk-circulant matrices (with geometric sequence), Some remarks on duality and optimality of a class of constrained convex quadratic minimization problems, Unnamed Item, Invariance and parallel sums, Geometric unfolding of synchronization dynamics on networks, On eigenvalue placement in linear time-invariant systems with input derivatives, Unnamed Item, On a question of Drazin, Hybrid (b, c)-inverses and five finiteness properties in rings, semigroups, and categories, The forward order laws for {1,2,3}- and {1,2,4}-inverses of a three matrix products, Explicit formulas and determinantal representation for η-skew-Hermitian solution to a system of quaternion matrix equations, Unnamed Item, Inverse complements and strongly unit regular elements, Characterizations and representations for the CMP inverse and its application, New classes of more general weighted outer inverses, An N-periodic control for coupled systems