An upper bound for the spectral condition number of a diagonalizable matrix
type: Item
instance of: scholarly article
title: An upper bound for the spectral condition number of a diagonalizable matrix
zbMATH Open document ID: 0877.15007
DOI: 10.1016/S0024-3795(97)80029-8
published in: Linear Algebra and its Applications
publication date: 1997-12-10T00:00:00Z
review text: A diagonalizable \(n\times n\) matrix \(A\), a transformation matrix \(P\) (defined by \(P^{-1}AP= J\), where \(J=\text{diag}(\lambda_1,\lambda_2,\dots,\lambda_n))\), and the spectral condition number \(\kappa(A)= \min_G |P|_2|P^{-1}|_2\), \(G=\{P\mid P^{-1}AP=J\}\), are considered. An upper bound of \(\kappa(A)\) is obtained from the elements of \(T\), the exact Schur form of \(A\). \(\kappa(A)\) is used to find the error bounds of eigenvalues and thus to estimate the accuracy of the computed eigenvalues. A numerical example is presented for illustration.
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 1040639
zbMATH Keywords: spectral condition number
zbMATH Keywords: error bounds
zbMATH Keywords: eigenvalues
zbMATH Keywords: numerical example
author: Erxiong Jiang
author: P. C. B. Lam
MaRDI profile type: Publication
cites work: Norms and exclusion theorems
cites work: Bounds for iterates, inverses, spectral variation and fields of values of non-normal matrices
cites work: On spectral variation of a nonnormal matrix
cites work: The condition numbers of the matrix eigenvalue problem
cites work: Q5674306
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description: scientific article; zbMATH DE number 1040639