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

10 Scopus citations

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 (US)
Pages (from-to)	517-525
Number of pages	9
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	35
Issue number	2
DOIs	https://doi.org/10.1137/130920897
State	Published - Jan 2014
Externally published	Yes

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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.",

author = "Jennifer Pestana",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: This work was supported by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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N2 - 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.

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.

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On the Eigenvalues and Eigenvectors of Block Triangular Preconditioned Block Matrices

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