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Digitale Medien

Low-rank revealing QR factorizations (1994)

Chan, Tony F. ; Hansen, Per Christian

New York, NY [u.a.] : Wiley-Blackwell

Numerical Linear Algebra with Applications 1 (1994), S. 33-44

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ISSN: 1070-5325

Schlagwort(e): Rank revealing QR factorization ; Column pivoting ; Numerical rank ; Subset selection ; Engineering ; Engineering General

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik

Notizen: Rank revealing factorizations are used extensively in signal processing in connection with, for example, linear prediction and signal subspace algorithms. We present an algorithm for computing rank revealing QR factorizations of low-rank matrices. The algorithm produces tight upper and lower bounds for all the largest singular values, thus making it particularly useful for treating rank deficient problems by means of subset selection, truncated QR, etc. The algorithm is similar in spirit to an algorithm suggested earlier by Chan for matrices with a small nullity, and it can also be considered as an extension of ordinary column pivoting.

Zusätzliches Material: 1 Ill.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/nla.1680010105

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Digitale Medien

Transpose-free formulations of Lanczos-type methods for nonsymmetric linear systems (1998)

Chan, Tony F. ; de Pillis, Lisette ; van der Vorst, Henk

Springer

Numerical algorithms 17 (1998), S. 51-66

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ISSN: 1572-9265

Schlagwort(e): Lanczos algorithm ; quasi-minimal residual algorithm ; bi-conjugate gradients algorithm ; nonsymmetric linear systems ; Krylov subspace methods ; 65F10 ; 65N20

Quelle: Springer Online Journal Archives 1860-2000

Thema: Informatik , Mathematik

Notizen: Abstract We present a transpose-free version of the nonsymmetric scaled Lanczos procedure. It generates the same tridiagonal matrix as the classical algorithm, using two matrix–vector products per iteration without accessing AT. We apply this algorithm to obtain a transpose-free version of the Quasi-minimal residual method of Freund and Nachtigal [15] (without look-ahead), which requires three matrix–vector products per iteration. We also present a related transpose-free version of the bi-conjugate gradients algorithm.