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Orthogonal polynomials and the Lanczos method

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Brezinski C., Sadok H., Redivo Zaglia M.

Banach Center Publications

1994

tom 29

nr 1

19-33

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.

Ograniczanie wyników

1 Banach Center Publications

1 Brezinski C.

1 Redivo Zaglia M.

1 Sadok H.

1 1994

Wyniki wyszukiwania

Orthogonal polynomials and the Lanczos method