Perturbation bounds of the Krylov bases and associated Hessenberg forms
type: Item
instance of: scholarly article
title: Perturbation bounds of the Krylov bases and associated Hessenberg forms
zbMATH Open document ID: 0884.15004
DOI: 10.1016/S0024-3795(96)00299-6
published in: Linear Algebra and its Applications
publication date: 1998-02-04T00:00:00Z
review text: The author proves a perturbation formula for orthonormal bases of the Krylov subspace span \([f_1,A_1f_1,\ldots,A_1^{j-1}f_1]\) for a matrix \(A_1\) and a vector \(f_1\), in terms of the condition number of an orthonormal basis for the unperturbed matrix and vector \(A,f\) and the \(L^2\) norms of \(A_1-A\), \(f_1-f\).
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 1076367
zbMATH Keywords: Krylov basis
zbMATH Keywords: Krylov subspace
zbMATH Keywords: perturbation of matrix
zbMATH Keywords: Hessenberg form
zbMATH Keywords: condition number
author: Sergey V. Kuznetsov
reviewed by: Ki Hang Kim
MaRDI profile type: Publication
cites work: The principle of minimized iterations in the solution of the matrix eigenvalue problem
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cites work: Condition number of the Krylov bases and subspaces
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cites work: Inertia characteristics of self-adjoint matrix polynomials
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full work available at URL: s0024-3795(96)00299-6
OpenAlex ID: W2000259795
Wikidata QID: Q127374502
description: scientific article; zbMATH DE number 1076367