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A fast symmetric SVD algorithm for square Hankel matrices
, 2007
"... This article was published in an Elsevier journal. The attached copy is furnished to the author for noncommercial research and education use, including for instruction at the author’s institution, sharing with colleagues and providing to institution administration. Other uses, including reproductio ..."
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This article was published in an Elsevier journal. The attached copy is furnished to the author for noncommercial research and education use, including for instruction at the author’s institution, sharing with colleagues and providing to institution administration. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright Author's personal copy Available online at www.sciencedirect.com
A Twisted Factorization Method for Symmetric SVD of a Complex Symmetric Tridiagonal Matrix
"... This paper presents an O(n 2) method based on twisted factorization for computing the Takagi vectors of an nbyn 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 th ..."
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This paper presents an O(n 2) method based on twisted factorization for computing the Takagi vectors of an nbyn 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. Our preliminary numerical experiments have confirmed our analysis and demonstrate the twisted factorization method is much more efficient than the implicit QR method, divideandconquer method and Matlab svd subroutine.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS Numer. Linear Algebra Appl. 2009; 16:801–815
"... A twisted factorization method for symmetric SVD of a complex symmetric tridiagonal matrix ..."
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A twisted factorization method for symmetric SVD of a complex symmetric tridiagonal matrix
A Takagi Factorization of a Real Symmetric Tridiagonal Matrix
"... This paper presents an explicit Takagi Factorization of a real symmetric tridiagonal matrix. ..."
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This paper presents an explicit Takagi Factorization of a real symmetric tridiagonal matrix.