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Orthogonal polynomials and the Lanczos method

100%

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.

Contractive projections on the fixed point set of $L_∞$ contractions

75%

Lin M., Sine R.

Colloquium Mathematicum

1991

tom 62

nr 1

91-96

Evaluating improvements of records

63%

Rychlik T.

Applicationes Mathematicae

1996-1997

tom 24

nr 3

315-324

We evaluate the extreme differences between the consecutive expected record values appearing in an arbitrary i.i.d. sample in the standard deviation units. We also discuss the relevant estimates for parent distributions coming from restricted families and other scale units.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Banach Center Publications

1 Colloquium Mathematicum

1 Brezinski C.

1 Lin M.

1 Redivo Zaglia M.

1 Rychlik T.

1 Sadok H.

1 Sine R.

1 1997

1 1994

1 1991

Wyniki wyszukiwania

Orthogonal polynomials and the Lanczos method

Contractive projections on the fixed point set of $L_∞$ contractions

Evaluating improvements of records