On the generation of Krylov subspace bases
type: Item
instance of: scholarly article
title: On the generation of Krylov subspace bases
zbMATH Open document ID: 1253.65049
author: Bernard Philippe
author: Lothar Reichel
published in: Applied Numerical Mathematics
publication date: 2012-07-13T00:00:00Z
review text: The authors discuss different ways for the construction of Krylov subspace bases used in the generalized minimal residual (GMRES) method for solving systems of linear equations \(A x = b\) approximately. Especially, the construction by means of shifted and scaled versions of the standard Chebyshev polynomials of the first kind and by means of scaled Newton polynomials is considered. Some numerical examples are presented. For different matrices \(A\) the condition numbers for the scaled power basis, two kinds of Newton bases and the Chebyshev polynomial basis are compared. Furthermore, the influence of the condition number of the Krylov subspace bases on the convergence of the GMRES method is illustrated. The discussed approaches are also applicable to Krylov subspace methods for eigenvalue computations and the evaluation of matrix functions.
reviewed by: Michael Jung
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F60
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 6055249
zbMATH Keywords: Krylov subspace basis
zbMATH Keywords: Arnoldi process
zbMATH Keywords: iterative method
zbMATH Keywords: generalized minimal residual method
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: Newton polynomials
zbMATH Keywords: numerical examples
zbMATH Keywords: condition numbers
zbMATH Keywords: convergence
zbMATH Keywords: eigenvalue computations
zbMATH Keywords: evaluation of matrix functions
describes a project that uses: eigs
describes a project that uses: ARPACK
describes a project that uses: Eigtool
MaRDI profile type: Publication
full work available at URL: j.apnum.2010.12.009
OpenAlex ID: W1970524119
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DOI: 10.1016/J.APNUM.2010.12.009
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