Displaying similar documents to “Avoiding look-ahead in the Lanczos method and Padé approximation”

An intoduction to formal orthogonality and some of its applications.

Claude Brezinski (2002)

RACSAM

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This paper is an introduction to formal orthogonal polynomials and their application to Padé approximation, Krylov subspace methods for the solution of systems of linear equations, and convergence acceleration methods. Some more general formal orthogonal polynomials, and the concept of biorthogonality and its applications are also discussed.

Zeroes of orthogonal polynomials by QD-algorithm

Jiří Fiala (1969)

Aplikace matematiky

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In the paper a method for computing zeroes of orthogonal polynomials is presented. An algorithm is given for computing directly the top row of the QD-scheme for some recurrently defined polynomials. The algorithm is then applied to classical orthogonal polynomials.

Orthogonal polynomials and the Lanczos method

C. Brezinski, H. Sadok, M. Redivo Zaglia (1994)

Banach Center Publications

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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...

A unified approach to some strategies for the treatment of breakdown in Lanczos-type algorithms

A. El Guennouni (1999)

Applicationes Mathematicae

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The Lanczos method for solving systems of linear equations is implemented by using some recurrence relationships between polynomials of a family of formal orthogonal polynomials or between those of two adjacent families of formal orthogonal polynomials. A division by zero can occur in these relations, thus producing a breakdown in the algorithm which has to be stopped. In this paper, three strategies to avoid this drawback are discussed: the MRZ and its variants, the normalized and unnormalized...