The Orthogonal qd-Algorithm

The orthogonal qd-algorithm is presented to compute the singular value decomposition of a bidiagonal matrix. This algorithm represents a modification of Rutishauser's qd-algorithm, and it is capable of determining all the singular values and their corresponding singular vectors to high relative...

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Bibliographic Details
Published in:SIAM journal on scientific computing Vol. 18; no. 4; pp. 1163 - 1186
Main Author: von Matt, Urs
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.07.1997
Subjects:
Accuracy
Algorithms
Decomposition
Eigenvalues
Hierarchies
Linear algebra
Matrix
ISSN:1064-8275, 1095-7197
Online Access:Get full text
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Summary:The orthogonal qd-algorithm is presented to compute the singular value decomposition of a bidiagonal matrix. This algorithm represents a modification of Rutishauser's qd-algorithm, and it is capable of determining all the singular values and their corresponding singular vectors to high relative accuracy. A generalization of the Givens transformation, which has applications besides the orthogonal qd-algorithm, is also introduced. The shift strategy of the orthogonal qd-algorithm is based on Laguerre's method, which is used to compute a lower bound on the smallest singular value of the bidiagonal matrix. Special attention is devoted to the numerically stable evaluation of this shift.
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ISSN:1064-8275
1095-7197
DOI:10.1137/S1064827594274887