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A twisted factorization method for symmetric SVD of a complex symmetric tridiagonal matrix
Author(s) -
Xu Wei,
Qiao Sanzheng
Publication year - 2009
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.642
Subject(s) - tridiagonal matrix , orthogonality , singular value decomposition , mathematics , matrix decomposition , qr decomposition , singular value , factorization , flops , matrix (chemical analysis) , divide and conquer algorithms , symmetric matrix , incomplete lu factorization , algebra over a field , algorithm , pure mathematics , computer science , parallel computing , geometry , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , composite material
This paper presents an O ( n 2 ) 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 ( n 2 ) flops, the total cost of symmetric singular value decomposition or the Takagi factorization is O ( n 2 ) 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.