A geometric theory for preconditioned inverse iteration. I: Extrema of Rayleigh quotient
type: Item
instance of: scholarly article
title: A geometric theory for preconditioned inverse iteration. I: Extrema of Rayleigh quotient
zbMATH Open document ID: 0976.65034
DOI: 10.1016/S0024-3795(00)00239-1
author: Klaus Neymeyr
published in: Linear Algebra and its Applications
publication date: 2001-05-13T00:00:00Z
review text: The method of preconditioned inverse iteration calculates some eigenvalues of large sparse matrices arising e.g. in finite element discretization of partial differential equations. The solution of linear equations in each step of the original inverse iteration is replaced by using a preconditioner, often a multigrid preconditioner. A convergence analysis is given in Part II [ibid. 322, No. 1-3, 87-104 (2001)]. It is based on several results derived in Part I, e.g. on the maximum of the Rayleigh-quotient, if the preconditioner lies in a certain class.
reviewed by: Ludwig Elsner
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 1559342
zbMATH Keywords: symmetric eigenvalue problem
zbMATH Keywords: preconditioning
zbMATH Keywords: preconditioned inverse iteration
zbMATH Keywords: eigenvalues
zbMATH Keywords: large sparse matrices
zbMATH Keywords: finite element
zbMATH Keywords: multigrid
zbMATH Keywords: convergence
zbMATH Keywords: Rayleigh-quotient
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1559342