scientific article

Publication date: 5 June 1993

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

perturbation theory Hermitian matrices error analysis LR algorithm QR algorithm matrix eigenvalue reduction to condensed form advanced exposition

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Iterative numerical methods for linear systems (65F10) Roundoff error (65G50) Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05) Canonical forms, reductions, classification (15A21) Orthogonalization in numerical linear algebra (65F25) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra (15-01)

Related Items (only showing first 100 items - show all)

Highly accurate verified error bounds for Krylov type linear system solvers ⋮ A spectral Chebyshev method for linear stability analysis of one-dimensional exact solutions of gas dynamics. ⋮ The Gauss quadrature for general linear functionals, Lanczos algorithm, and minimal partial realization ⋮ A pseudo-Hermitian \(\beta\)-Hermite family of matrices ⋮ Duality of graded graphs ⋮ Lanczos algorithm for the quadratic eigenvalue problem in engineering applications ⋮ Deflated preconditioned conjugate gradient solvers for linear elasticity ⋮ Multivariate nonparametric test of independence ⋮ Algebraic properties of Manin matrices. I ⋮ Hierarchical matrix approximation with blockwise constraints ⋮ A fast and stable parallel QR algorithm for symmetric tridiagonal matrices ⋮ A note on the eigenvectors of perturbed matrices with applications to linear positive systems ⋮ Local analysis of a spectral correction for the Gauss-Newton model applied to quadratic residual problems ⋮ On a sub‐Stiefel Procrustes problem arising in computer vision ⋮ Acoustic boundary element eigenproblem with sound absorption and its solution using Lanczos algorithm ⋮ Effect of shear deformation on the buckling parameter of perforated and non-perforated plates studied using the boundary element method ⋮ A refined variant of the inverse-free Krylov subspace method for symmetric generalized eigenvalue problems ⋮ High level synthesis FPGA implementation of the Jacobi algorithm to solve the eigen problem ⋮ An iterative approach for nonproportionally damped systems ⋮ Computing the roots of sparse high-degree polynomials that arise from the study of random simplicial complexes ⋮ Fast solution of Schrödinger's equation using linear combinations of plane waves ⋮ A tensor format for the generalized Hessenberg method for solving Sylvester tensor equations ⋮ Stochastic epidemic models with random environment: quasi-stationarity, extinction and final size ⋮ A parallel algorithm for evaluating general linear recurrence equations ⋮ An extended Hamiltonian QR algorithm ⋮ The Lanczos algorithm applied to unsymmetric generalized eigenvalue problem ⋮ Optimal sparse volatility matrix estimation for high-dimensional Itô processes with measurement errors ⋮ Calculating a function of a matrix with a real spectrum ⋮ Fitting helices to data by total least squares ⋮ On perturbations of principal eigenvectors of substochastic matrices ⋮ Inequalities for the eigenvectors associated to extremal eigenvalues in rank one perturbations of symmetric matrices ⋮ Stable generalized finite element method and associated iterative schemes; application to interface problems ⋮ TRAX: An approach for the time rational analysis of complex dynamic systems ⋮ A Lanczos-type procedure for tensors ⋮ An iterative algorithm for computing mean first passage times of Markov chains ⋮ Stable generalized finite element method (SGFEM) ⋮ A class of quasi-variational inequalities for adaptive image denoising and decomposition ⋮ A necessary condition for dispersal driven growth of populations with discrete patch dynamics ⋮ Fractional cosine and sine transforms over finite fields ⋮ Deflated preconditioned conjugate gradients applied to a Petrov-Galerkin generalized least squares finite element formulation for incompressible flows with heat transfer ⋮ Stochastic analysis of the motion of DNA nanomechanical bipeds ⋮ An upper \(J\)-Hessenberg reduction of a matrix through symplectic Householder transformations ⋮ Chebyshev rootfinding via computing eigenvalues of colleague matrices: when is it stable? ⋮ Ramanujan theta functions and birth and death processes ⋮ A unification of unitary similarity transforms to compressed representations ⋮ A reduced spectral function approach for the stochastic finite element analysis ⋮ Estimating the characteristics of the accuracy and computational complexity in approximate methods of global optimization of nonlinear functionals ⋮ Equivalence between modified symplectic Gram-Schmidt and Householder SR algorithms ⋮ Growth in Gaussian elimination for weighing matrices, \(W (n, n-1)\) ⋮ A correction of approximations used in sensitivity study of principal component analysis ⋮ Coupled map model with a conserved order parameter ⋮ Computing with barycentric polynomials ⋮ An adaptive subdivision method for root finding of univariate polynomials ⋮ Phase diagram of the chromatic polynomial on a torus ⋮ Iterative solution applied to the Helmholtz equation: complex deflation on unstructured grids ⋮ The block Hessenberg process for matrix equations ⋮ On the stability of polynomial transformations between Taylor, Bernstein and Hermite forms ⋮ Enclosure of all index-1 saddle points of general nonlinear functions ⋮ An Arnoldi-based iterative scheme for nonsymmetric matrix pencils arising in finite element stability problems ⋮ Stability of multiple-pulse solutions ⋮ Accurate polynomial root-finding methods for symmetric tridiagonal matrix eigenproblems ⋮ Symplectic Householder transformations for a QR-like decomposition, a geometric and algebraic approaches ⋮ General constraint preconditioning iteration method for singular saddle-point problems ⋮ Deflated block Krylov subspace methods for large scale eigenvalue problems ⋮ On the growth problem for skew and symmetric conference matrices ⋮ On computation of real eigenvalues of matrices via the Adomian decomposition ⋮ Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case ⋮ Correlation analysis of enzymatic reaction of a single protein molecule ⋮ Topology-guided sampling of nonhomogeneous random processes ⋮ An explicit formula for Lanczos polynomials ⋮ On the stability of transformations between power and Bernstein polynomial forms ⋮ Solving eigenvalue problems by implicit decomposition ⋮ Transient response analysis of randomly parametrized finite element systems based on approximate balanced reduction ⋮ The relative accuracy of \(\mathtt{(x+y)*(x-y)}\) ⋮ Nearest \(\Omega \)-stable matrix via Riemannian optimization ⋮ A fast algorithm for index of annihilation computations ⋮ A reduced polynomial chaos expansion method for the stochastic finite element analysis ⋮ Boundary sampled-data feedback stabilization for parabolic equations ⋮ Commutation relations and Markov chains ⋮ A secular equation for the eigenvalues of a diagonal matrix perturbation ⋮ Validated Saddle-Node Bifurcations and Applications to Lattice Dynamical Systems ⋮ A computational method for finding the zeros of a multivariable linear time invariant system ⋮ A treatment of breakdowns and near breakdowns in a reduction of a matrix to upper \(J\)-Hessenberg form and related topics ⋮ Implicit QR algorithms for palindromic and even eigenvalue problems ⋮ On the stability of equilibrium states of the dynamical systems in critical cases ⋮ Theory and applications of financial chaos index ⋮ Using reserves of computing optimization to solve complex problems ⋮ Diffraction from arbitrarily shaped bodies of revolution: Analytical regularization ⋮ The simpler block CMRH method for linear systems ⋮ On the \(Q\)-order of convergence for coupled sequences arising in iterative numerical processes ⋮ Optimal control of dynamic systems: application to spline approximations ⋮ Constrained stability of conservative static equilibrium ⋮ Values of minors of some infinite families of matrices constructed from supplementary difference sets and their application to the growth problem ⋮ Semi-supervised generalized eigenvalues classification ⋮ Nondifferentiable optimization algorithm for designing control systems having singular value inequalities ⋮ A tutorial history of least squares with applications to astronomy and geodesy ⋮ Simplification of solving diagnostics problems by convolution of applied Markovian models into the quantum representations ⋮ Decompositions and coalescing eigenvalues of symmetric definite pencils depending on parameters ⋮ Evaluation of the characteristic polynomial of a graph ⋮ A spectral approach for fuzzy uncertainty propagation in finite element analysis

This page was built for publication: