Methods and algorithms of solving spectral problems for polynomial and rational matrices
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Publication:1389295
DOI10.1007/BF02168360zbMath0928.65064MaRDI QIDQ1389295
Publication date: 22 June 1998
Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)
algorithmspolynomial matricesnonlinear eigenvalue problemsrank factorizationelliptic spectral problemspolynomial spectral problems
Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)
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Uses Software
Cites Work
- Properties of the system matrix of a generalized state-space system†
- A Jordan Factorization Theorem for Polynomial Matrices
- A Hessenberg-Schur method for the problem AX + XB= C
- A Schur method for solving algebraic Riccati equations
- An Algorithm for Numerical Computation of the Jordan Normal Form of a Complex Matrix
- On the Separation of Two Matrices
- Accelerated Gauss-Newton algorithms for nonlinear least squares problems
- The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimators
- Fitting Empirical Data by Positive Sums of Exponentials
- Factorizations of Transfer Functions
- The generalized eigenstructure problem in linear system theory
- A Generalized Eigenvalue Approach for Solving Riccati Equations
- Properties of numerical algorithms related to computing controllability
- Algorithms for Separable Nonlinear Least Squares Problems
- Numerical Solution of a Quadratic Matrix Equation
- The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
- Towards a Generalized Singular Value Decomposition
- A relationship between sensitivity and stability of multivariable feedback systems
- Solving Symmetric-Definite Quadratic $\lambda $-Matrix Problems without Factorization
- Algorithm 590: DSUBSP and EXCHQZ : FORTRAN Subroutines for Computing Deflating Subspaces with Specified Spectrum
- Distributed and Shared Memory Block Algorithms for the Triangular Sylvester Equation with $\operatorname{sep}^{ - 1} $ Estimators
- Numerical Considerations in Computing Invariant Subspaces
- Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
- Gershgorin Theory for the Generalized Eigenvalue Problem Ax = λBx
- 𝑆𝑂𝑅-methods for the eigenvalue problem with large sparse matrices
- Simultaneous Iteration for Partial Eigensolution of Real Matrices
- A General Matrix Eigenvalue Algorithm
- Iterative Solution of the Generalized Eigenvalue Problem
- Generalizing the Singular Value Decomposition
- Ill-Conditioned Eigensystems and the Computation of the Jordan Canonical Form
- Some Thoughts on the QZ Algorithm for Solving the Generalized Eigenvalue Problem
- Solution of Non-linear Eigenvalue Problems by the Continuation Method
- Perturbation Bounds for the $QR$ Factorization of a Matrix
- The Algebraic Theory of Matrix Polynomials
- Generalized Eigenvalue Problems for Rectangular Matrices
- Algorithms for Solvents of Matrix Polynomials
- A propos de l’algorithme $QZ$
- Generalized Schur methods with condition estimators for solving the generalized Sylvester equation
- LAPACK-style algorithms and software for solving the generalized Sylvester equation and estimating the separation between regular matrix pairs
- $Ax = \lambda Bx$ and the Generalized Eigenproblem
- Zur Theorie der λ-Matrizen
- Singular functions of polynomial matrices
- Solving eigenvalue problems for two-parameter polynomial matrices. Methods and algorithms. Part I.
- Experience with a Matrix Norm Estimator
- Analytic properties of the singular values of a rational matrix
- The Condition Number of Equivalence Transformations That Block Diagonalize Matrix Pencils
- Structural properties of linear dynamical systems
- Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
- Irreducible Realizations and the Degree of a Rational Matrix
- Calculating the Singular Values and Pseudo-Inverse of a Matrix
- The Rotation of Eigenvectors by a Perturbation. III
- Perturbation bounds for means of eigenvalues and invariant subspaces
- On an Approach to the Solution of the Generalized Latent Value Problem for $\lambda $-Matrices
- Numerical Linear Algebra
- On the Sensitivity of the Eigenvalue Problem $Ax = \lambda Bx$
- An Algorithm for Generalized Matrix Eigenvalue Problems
- An algorithm for numerical determination of the structure of a general matrix
- Algorithms for the Nonlinear Eigenvalue Problem
- The singular pencil of a linear dynamical system†
- The method of conjugate gradients used in inverse iteration
- Rang revealing QR factorizations
- The generalized eigenvalue problem and acoustic surface wave computations
- The codimension of singular matrix pairs
- The computation of Kronecker's canonical form of a singular pencil
- Rational Krylov sequence methods for eigenvalue computation
- Multiparameter eigenvalue problems. Volume I: Matrices and compact operators
- Inversion of lamdba-matrices and application to the theory of linear vibrations
- AB-algorithm and its modifications for the spectral problems of linear pencils of matrices
- Computing the CS and the generalized singular value decompositions
- The Lanczos-Arnoldi algorithm and controllability
- The generalized singular value decomposition and the general (A-\(\lambda\) B)-problem
- Perturbation bounds for the Cholesky and QR factorizations
- Matrices and indefinite scalar products
- Numerical aspects of Gram-Schmidt orthogonalization of vectors
- Computing the CS decomposition of a partitioned orthonormal matrix
- Solving nonlinear eigenvalue problems by algorithmic differentiation
- On perturbations and the equivalence orbit of a matrix pencil
- Lanczos algorithms and field of value rotations for symmetric matrix pencils
- Computing stable eigendecompositions of matrices
- Computing stable eigendecompositions of matrix pencils
- An improved algorithm for the computation of Kronecker's canonical form of a singular pencil
- The weak and strong stability of algorithms in numerical linear algebra
- Minimal factorization of matrix and operator functions
- An accelerated subspace iteration method
- On rank-deficient pseudoinverses
- Kronecker's canonical form and the QZ algorithm
- Pole assignment via Sylvester's equation
- Solving sparse symmetric definite quadratic lambda-matrix problems
- Computation of zeros of linear multivariable systems
- An Arnoldi-based iterative scheme for nonsymmetric matrix pencils arising in finite element stability problems
- Componentwise perturbation bounds for some matrix decompositions
- The roots of matrix pencils \((Ay=\lambda By)\): Existence, calculations, and relations to game theory
- On the closeness of eigenvalues and singular values for almost normal matrices
- Iterative eigenvalue algorithms based on convergent splittings
- Matrix eigensystem routines - EISPACK guide. 2nd ed
- On the latent roots of \(\lambda\)matrices
- A fundamental theorem on lambda-matrices with applications. I: Ordinary differential equations with constant coefficients
- Relative factorization of polynomials of several variables
- Spectral problems for pencils of polynomial matrices. Methods and algorithms. V
- Parallel and large-scale matrix computations in control: Some ideas
- On roots of functional lambda matrices
- The eigenstructure of an arbitrary polynomial matrix: Computational aspects
- The AB-algorithm and its properties
- The singular-function method for computing the eigenvalues of polynomial matrices
- On eigenvalues of matrices dependent on a parameter
- Nonlinear eigenvalue problems
- The solution of characteristic value-vector problems by Newton's method
- Singular value decomposition and least squares solutions
- Computational aspects of F. L. Bauer's simultaneous iteration method
- A gradient method for the matrix eigenvalue problem \(Ax = \lambda Bx\)
- An Algorithm for Computing Reducing Subspaces by Block Diagonalization
- On the Perturbation of LU, Cholesky, and QR Factorizations
- A New Algorithm for Numerical Path Following Applied to an Example from Hydrodynamical Flow
- Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems
- Fundamental, reachability, and observability matrices for discrete descriptor systems
- On Kublanovskaya’s Approach to the Solution of the Generalized Latent Value Problem for Functional $\lambda $-Matrices
- Chebyshev Acceleration Techniques for Solving Nonsymmetric Eigenvalue Problems
- A LINPACK-style condition estimator for the equation<tex>AX-XB^{T} = C</tex>
- The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses
- Computation of eigenpairs of for vibrations of spinning deformable bodies
- Accurate Singular Values of Bidiagonal Matrices
- Algorithm 598
- A method for eigenvalues of sparse λ-matrices
- Perturbation Analysis for the Generalized Singular Value Problem
- Polynomial matrices and feedback
- RGSVD—AN Algorithm for Computing the Kronecker Structure and Reducing Subspaces of Singular $A - \lambda B$ Pencils
- Residual Inverse Iteration for the Nonlinear Eigenvalue Problem
- Data-flow algorithms for parallel matrix computation
- Computing the Generalized Singular Value Decomposition
- Numerical Solution of Matrix Polynomial Equations by Newton's Method
- Accurate Solutions of Ill-Posed Problems in control theory
- The Numerical Solution of Higher Index Linear Time Varying Singular Systems of Differential Equations
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