NDLI: A comparison between the complex symmetric based and classical computation of the singular value decomposition of normal matrices

Content Provider	Springer Nature Link
Author	Ferranti, Micol Le, Thanh Hieu Vandebril, Raf
Copyright Year	2013
Abstract	An algorithm for computing the singular value decomposition of normal matrices using intermediate complex symmetric matrices is proposed. This algorithm, as most eigenvalue and singular value algorithms, consists of two steps. It is based on combining the unitarily equivalence of normal matrices to complex symmetric tridiagonal form with the symmetric singular value decomposition of complex symmetric matrices. Numerical experiments are included comparing several algorithms, with respect to speed and accuracy, for computing the symmetric singular value decomposition (also known as the Takagi factorization). Next we compare the novel approach with the classical Golub-Kahan method for computing the singular value decomposition of normal matrices: it is faster, consumes less memory, but on the other hand the results are significantly less accurate.
Starting Page	109
Ending Page	120
Page Count	12
File Format	PDF
ISSN	10171398
Journal	Numerical Algorithms
Volume Number	67
Issue Number	1
e-ISSN	15729265
Language	English
Publisher	Springer US
Publisher Date	2013-10-11
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Singular value decomposition Symmetric singular value decomposition Takagi factorization Normal matrix Numeric Computing Algorithms Algebra Theory of Computation Numerical Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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A comparison between the complex symmetric based and classical computation of the singular value decomposition of normal matrices