Orthogonal polynomials and the Lanczos method

• Autorzy: C. Brezinski , H. Sadok , M. Redivo Zaglia
• Języki publikacji: EN

Abstrakty

EN

Lanczos method for solving a system of linear equations is well known. It is derived from a generalization of the method of moments and one of its main interests is that it provides the exact answer in at most n steps where n is the dimension of the system. Lanczos method can be implemented via several recursive algorithms known as Orthodir, Orthomin, Orthores, Biconjugate gradient,... In this paper, we show that all these procedures can be explained within the framework of formal orthogonal polynomials. This theory also provides a natural basis for curing breakdown and near-breakdown in these algorithms. The case of the conjugate gradient squared method can be treated similarly.

Słowa kluczowe

EN

projection; biconjugate gradient; orthogonal polynomials; Lanczos method

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1994
• Tom: 29
• Numer: 1
• Strony: 19-33

Daty

wydano

1994

Twórcy

autor

C. Brezinski

• Laboratoire d'Analyse Numérique et d'Optimisation, UFR IEEA-M3, Université des Sciences et Technologies de Lille, F-59655 Villeneuve d'Ascq Cedex, France

autor

H. Sadok

• Laboratoire d'Analyse Numérique et d'Optimisation, UFR IEEA-M3, Université des Sciences et Technologies de Lille, F-59655 Villeneuve d'Ascq Cedex, France

autor

M. Redivo Zaglia

• Dipartimento di Elettronica e Informatica, Università degli Studi di Padova, Via Gradenigo 6/a, I-35131 Padova, Italy

Bibliografia

• [1] C. Brezinski, Padé-type Approximation and General Orthogonal Polynomials, Internat. Ser. Number. Math. 50, Birkhäuser, Basel 1980.
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• [5] C. Brezinski and M. Redivo Zaglia, Treatment of near-breakdown in the CGS algorithm, to appear.
• [6] C. Brezinski, M. Redivo Zaglia and H. Sadok, A breakdown-free Lanczos type algorithm for solving linear systems, Numer. Math. 63 (1992), 29-38.
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