A Parallel Algorithm for the Reduction to Tridiagonal Form for Eigendecomposition

One-sided orthogonal transformations which orthogonalize columns of a matrix are related to methods for finding singular values. They have the advantages of lending themselves to parallel and vector implementations and simplifying access to the data by not requiring access to both rows and columns....

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Bibliographic Details
Published in:SIAM journal on scientific computing Vol. 21; no. 3; pp. 987 - 1005
Main Authors: Hegland, Markus, Kahn, Margaret, Osborne, Michael
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 1999
Subjects:
Algorithms
Communication
Computers
Eigenvalues
Eigenvectors
Linear algebra
Matrix
ISSN:1064-8275, 1095-7197
Online Access:Get full text
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Summary:One-sided orthogonal transformations which orthogonalize columns of a matrix are related to methods for finding singular values. They have the advantages of lending themselves to parallel and vector implementations and simplifying access to the data by not requiring access to both rows and columns. They can be used to find eigenvalues when the matrix is given in factored form. Here, a finite sequence of transformations leading to a partial orthogonalization of the columns is described. This permits a tridiagonal matrix whose eigenvalues are the squared singular values to be derived. The implementation on the Fujitsu VPP series is discussed and some timing results are presented.
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ISSN:1064-8275
1095-7197
DOI:10.1137/S1064827595296719