Computing approximate eigenpairs of symmetric block tridiagonal matrices

Wilfried N. Gansterer; Robert C. Ward; Richard P. Muller; William A. Goddard

doi:10.1137/S1064827501399432

Computing approximate eigenpairs of symmetric block tridiagonal matrices

Wilfried N. Gansterer
, Robert C. Ward
, Richard P. Muller
, William A. Goddard

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

Abstract

A divide-and-conquer method for computing approximate eigenvalues and eigenvectors of a block tridiagorial matrix is presented. In contrast to a method described earlier [W. N. Gansterer, R. C. Ward, and R. P. Muller, ACM Trans. Math. Software, 28 (2002), pp. 45-58], the off-diagonal blocks can have arbitrary ranks. It is shown that lower rank approximations of the off-diagonal blocks as well as relaxation of deflation criteria permit the computation of approximate eigenpairs with prescribed accuracy at significantly reduced computational cost compared to standard methods such as, for example, implemented in LAPACK.

Original language	English
Pages (from-to)	65-85
Number of pages	21
Journal	SIAM Journal on Scientific Computing
Volume	25
Issue number	1
DOIs	https://doi.org/10.1137/S1064827501399432
Publication status	Published - 1 Jan 2003
Externally published	Yes

Keywords

Approximate eigenpairs
Block tridiagonal matrix
Divide-and-conquer method
Eigenvalue problem

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10.1137/S1064827501399432

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title = "Computing approximate eigenpairs of symmetric block tridiagonal matrices",

abstract = "A divide-and-conquer method for computing approximate eigenvalues and eigenvectors of a block tridiagorial matrix is presented. In contrast to a method described earlier [W. N. Gansterer, R. C. Ward, and R. P. Muller, ACM Trans. Math. Software, 28 (2002), pp. 45-58], the off-diagonal blocks can have arbitrary ranks. It is shown that lower rank approximations of the off-diagonal blocks as well as relaxation of deflation criteria permit the computation of approximate eigenpairs with prescribed accuracy at significantly reduced computational cost compared to standard methods such as, for example, implemented in LAPACK.",

keywords = "Approximate eigenpairs, Block tridiagonal matrix, Divide-and-conquer method, Eigenvalue problem",

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year = "2003",

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doi = "10.1137/S1064827501399432",

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AU - Gansterer, Wilfried N.

AU - Ward, Robert C.

AU - Muller, Richard P.

AU - Goddard, William A.

PY - 2003/1/1

Y1 - 2003/1/1

N2 - A divide-and-conquer method for computing approximate eigenvalues and eigenvectors of a block tridiagorial matrix is presented. In contrast to a method described earlier [W. N. Gansterer, R. C. Ward, and R. P. Muller, ACM Trans. Math. Software, 28 (2002), pp. 45-58], the off-diagonal blocks can have arbitrary ranks. It is shown that lower rank approximations of the off-diagonal blocks as well as relaxation of deflation criteria permit the computation of approximate eigenpairs with prescribed accuracy at significantly reduced computational cost compared to standard methods such as, for example, implemented in LAPACK.

AB - A divide-and-conquer method for computing approximate eigenvalues and eigenvectors of a block tridiagorial matrix is presented. In contrast to a method described earlier [W. N. Gansterer, R. C. Ward, and R. P. Muller, ACM Trans. Math. Software, 28 (2002), pp. 45-58], the off-diagonal blocks can have arbitrary ranks. It is shown that lower rank approximations of the off-diagonal blocks as well as relaxation of deflation criteria permit the computation of approximate eigenpairs with prescribed accuracy at significantly reduced computational cost compared to standard methods such as, for example, implemented in LAPACK.

KW - Approximate eigenpairs

KW - Block tridiagonal matrix

KW - Divide-and-conquer method

KW - Eigenvalue problem

UR - https://www.scopus.com/pages/publications/1842531885

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DO - 10.1137/S1064827501399432

M3 - Article

AN - SCOPUS:1842531885

SN - 1064-8275

VL - 25

SP - 65

EP - 85

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 1

ER -

Computing approximate eigenpairs of symmetric block tridiagonal matrices

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Keywords

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