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

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

Abstract

Block lower triangular matrices and block upper triangular matrices are popular preconditioners for 2×2 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. © 2014 Society for Industrial and Applied Mathematics.

Original language	English
Pages (from-to)	517-525
Number of pages	8
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	35
Issue number	2
DOIs	https://doi.org/10.1137/130920897
Publication status	Published - 2014

Keywords

Block triangular preconditioner
Convergence
Eigenvalues
Eigenvectors
Iterative method
Saddle point system

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10.1137/130920897

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abstract = "Block lower triangular matrices and block upper triangular matrices are popular preconditioners for 2×2 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. {\textcopyright} 2014 Society for Industrial and Applied Mathematics.",

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AB - Block lower triangular matrices and block upper triangular matrices are popular preconditioners for 2×2 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. © 2014 Society for Industrial and Applied Mathematics.

KW - Block triangular preconditioner

KW - Convergence

KW - Eigenvalues

KW - Eigenvectors

KW - Iterative method

KW - Saddle point system

U2 - 10.1137/130920897

DO - 10.1137/130920897

M3 - Article

SN - 0895-4798

VL - 35

SP - 517

EP - 525

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 2

ER -

On the eigenvalues and eigenvectors of block triangular preconditioned block matrices

Abstract

Keywords

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