Backward Error Analysis of Polynomial Eigenvalue Problems Solved by Linearization

DOI10.1137/15M1015777zbMath1382.65101MaRDI QIDQ2790065

Paul Van Dooren, Marc Van Barel, Piers W. Lawrence

Publication date: 2 March 2016

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

stabilitylinearizationstrong linearizationbackward errorpolynomial eigenvalue problemdual minimal basis

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (10)

Block Kronecker linearizations of matrix polynomials and their backward errors ⋮ A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error ⋮ Structured backward errors in linearizations ⋮ Constructing Strong Linearizations of Matrix Polynomials Expressed in Chebyshev Bases ⋮ The infinite Lanczos method for symmetric nonlinear eigenvalue problems ⋮ Chebyshev rootfinding via computing eigenvalues of colleague matrices: when is it stable? ⋮ On the backward error incurred by the compact rational Krylov linearization ⋮ Robustness and perturbations of minimal bases. II: The case with given row degrees ⋮ Polynomial eigenvalue solver based on tropically scaled Lagrange linearization ⋮ Robustness and perturbations of minimal bases

Uses Software

• LAPACK

Cites Work

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