Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation

DOI10.1016/S0024-3795(00)00272-XzbMath0978.65026MaRDI QIDQ5929749

Shin'ichi Oishi

Publication date: 12 February 2002

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

perturbation theorynumerical examplesBauer-Fike type theoremMATLABrounding mode controlled computationverified eigenvalue computationverified singular value computationWeyl type theorem

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Inequalities involving eigenvalues and eigenvectors (15A42) Algorithms with automatic result verification (65G20)

Related Items (13)

Tight and efficient enclosure of matrix multiplication by using optimized BLAS ⋮ Iterative refinement for symmetric eigenvalue decomposition ⋮ Fast enclosure for all eigenvalues in generalized eigenvalue problems ⋮ Fast verified solutions of linear systems ⋮ Computing eigenvalues of the Laplacian on rough domains ⋮ Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh-Ritz procedure for generalized Hermitian eigenvalue problems ⋮ Fast simulation for Gaussian random fields on compact Riemannian manifolds ⋮ Fast algorithms for floating-point interval matrix multiplication ⋮ Unnamed Item ⋮ Solving a sparse system using linear algebra ⋮ Verified bounds for all the singular values of matrix ⋮ Fast inclusion of interval matrix multiplication ⋮ Iterative refinement for symmetric eigenvalue decomposition. II. Clustered eigenvalues

Uses Software

• Matlab

Cites Work

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• Norms and exclusion theorems
• Fast verification of solutions of matrix equations
• Relative Perturbation Techniques for Singular Value Problems
• Calculating the Singular Values and Pseudo-Inverse of a Matrix

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