A Lanczos bidiagonalization algorithm for Hankel matrices

This paper presents a fast algorithm for bidiagonalizing a Hankel matrix. An m × n Hankel matrix is reduced to a real bidiagonal matrix in O ( ( m + n ) n log ( m + n ) ) floating-point operations (flops) using the Lanczos method with modified partial orthogonalization and reset schemes to improve i...

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Bibliographic Details
Published in:Linear algebra and its applications 2009-03, Vol.430 (5), p.1531-1543
Main Authors: Browne, Kevin, Qiao, Sanzheng, Wei, Yimin
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Fast Hankel SVD
Hankel matrix
Lanczos bidiagonalization
Linear and multilinear algebra, matrix theory
Mathematics
Sciences and techniques of general use
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Summary:This paper presents a fast algorithm for bidiagonalizing a Hankel matrix. An m × n Hankel matrix is reduced to a real bidiagonal matrix in O ( ( m + n ) n log ( m + n ) ) floating-point operations (flops) using the Lanczos method with modified partial orthogonalization and reset schemes to improve its stability. Performance improvement is achieved by exploiting the Hankel structure, as fast Hankel matrix–vector multiplication is used. The accuracy and efficiency of the algorithm are demonstrated by our numerical experiments.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2008.01.012