A twisted factorization method for symmetric SVD of a complex symmetric tridiagonal matrix

This paper presents an O(n2) method based on the twisted factorization for computing the Takagi vectors of an n‐by‐n complex symmetric tridiagonal matrix with known singular values. Since the singular values can be obtained in O(n2) flops, the total cost of symmetric singular value decomposition or...

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Bibliographic Details
Published in:Numerical linear algebra with applications 2009-10, Vol.16 (10), p.801-815
Main Authors: Xu, Wei, Qiao, Sanzheng
Format: Article
Language:English
Subjects:
Accuracy
complex symmetric matrix
Decomposition
Factorization
fast SVD
Mathematical analysis
Mathematical models
Matlab
Orthogonality
symmetric SVD
Takagi factorization
twisted factorization
Vectors (mathematics)
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Summary:This paper presents an O(n2) method based on the twisted factorization for computing the Takagi vectors of an n‐by‐n complex symmetric tridiagonal matrix with known singular values. Since the singular values can be obtained in O(n2) flops, the total cost of symmetric singular value decomposition or the Takagi factorization is O(n2) flops. An analysis shows the accuracy and orthogonality of Takagi vectors. Also, techniques for a practical implementation of our method are proposed. Our preliminary numerical experiments have verified our analysis and demonstrated that the twisted factorization method is much more efficient than the implicit QR method, divide‐and‐conquer method and Matlab singular value decomposition subroutine with comparable accuracy. Copyright © 2009 John Wiley & Sons, Ltd.
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.642