On the eigenvalues and eigenvectors of block triangular preconditioned block matrices

Jennifer Pestana

doi:10.1137/130920897

On the eigenvalues and eigenvectors of block triangular preconditioned block matrices

Jennifer Pestana

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

119 Downloads (Pure)

Abstract

Block lower triangular matrices and block upper triangular matrices are popular preconditioners for $2\times 2$ block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related.

Original language	English
Pages (from-to)	517-525
Number of pages	8
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	35
Early online date	24 Apr 2014
DOIs	https://doi.org/10.1137/130920897
Publication status	E-pub ahead of print - 24 Apr 2014

Keywords

block triangluar preconditioner
convergence
eigenvalues
eigenvectors
iterative method
saddle point system

Access to Document

10.1137/130920897

Pestana-SIAMJMAA2014-on-the-eigenvalues-and-eigenvectors-of-block-triangularAccepted author manuscript, 297 KB

Cite this

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title = "On the eigenvalues and eigenvectors of block triangular preconditioned block matrices",

abstract = "Block lower triangular matrices and block upper triangular matrices are popular preconditioners for $2\times 2$ block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related.",

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AB - Block lower triangular matrices and block upper triangular matrices are popular preconditioners for $2\times 2$ block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related.

KW - block triangluar preconditioner

KW - convergence

KW - eigenvalues

KW - eigenvectors

KW - iterative method

KW - saddle point system

U2 - 10.1137/130920897

DO - 10.1137/130920897

M3 - Article

VL - 35

SP - 517

EP - 525

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

SN - 0895-4798

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