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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Vydané v:SIAM journal on scientific computing Ročník 18; číslo 4; s. 1163 - 1186
Hlavný autor: von Matt, Urs
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Philadelphia Society for Industrial and Applied Mathematics 01.07.1997
Predmet:
Accuracy
Algorithms
Decomposition
Eigenvalues
Hierarchies
Linear algebra
Matrix
ISSN:1064-8275, 1095-7197
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Shrnutí: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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1064-8275
1095-7197
DOI:10.1137/S1064827594274887