Perturbation of Eigenvalues for Matrix Polynomials via The Bauer--Fike Theorems

DOI10.1137/S0895479802217928zbMath1054.15021MaRDI QIDQ4443844

Eric King-Wah Chu

Publication date: 19 January 2004

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

zbMATH Keywords

eigenvalue problemcondition numbersecond-order systemperturbation analysisquadratic eigenvalue problemmatrix polynomialmultiple eigenvalueslambda-matrixBauer--Fike theorem

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) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12) Numerical solutions to inverse eigenvalue problems (65F18) Matrix pencils (15A22)

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Implicitly Restarted Refined Partially Orthogonal Projection Method with Deflation ⋮ Perturbation analysis of matrices over a quaternion division algebra ⋮ Vibration of fast trains, palindromic eigenvalue problems and structure-preserving doubling algorithms ⋮ On condition numbers of polynomial eigenvalue problems ⋮ Structured eigenvalue condition numbers and linearizations for matrix polynomials ⋮ PERTURBATION RESULTS RELATED TO PALINDROMIC EIGENVALUE PROBLEMS ⋮ Localization Theorems for Nonlinear Eigenvalue Problems ⋮ Implicitly Restarted Refined Generalised Arnoldi Method with Deflation for the Polynomial Eigenvalue Problem ⋮ Perturbation of eigenvalues for periodic matrix pairs via the Bauer-Fike theorems ⋮ A novel method to compute all eigenvalues of the polynomial eigenvalue problems in an open half plane

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