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

6 Citations (Scopus)

83 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

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Pestana, J. (2014). On the eigenvalues and eigenvectors of block triangular preconditioned block matrices. SIAM Journal on Matrix Analysis and Applications, 35, 517-525. https://doi.org/10.1137/130920897

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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.

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KW - eigenvalues

KW - eigenvectors

KW - iterative method

KW - saddle point system

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