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1

Orthogonal polynomials and the Lanczos method

100%

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

Banach Center Publications

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1994

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tom 29

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nr 1

19-33

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.

2

Altman's methods revisited

100%

Roland C., Beckermann B., Brezinski C.

Applicationes Mathematicae

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2004

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tom 31

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nr 3

353-368

EN

We discuss two different methods of Altman for solving systems of linear equations. These methods can be considered as Krylov subspace type methods for solving a projected counterpart of the original system. We discuss the link to classical Krylov subspace methods, and give some theoretical and numerical results on their convergence behavior.

3

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Bordering methods and progressive forms for sequence transformations

86%

Brezinski C.

Applicationes Mathematicae

|

1988

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tom 20

|

nr 3

435-443

Ograniczanie wyników

2 Applicationes Mathematicae

1 Banach Center Publications

3 Brezinski C.

1 Beckermann B.

1 Redivo Zaglia M.

1 Roland C.

1 Sadok H.

1 2004

1 1994

1 1988

Orthogonal polynomials and the Lanczos method

Altman's methods revisited

Bordering methods and progressive forms for sequence transformations