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1999 | 26 | 1 | 33-62
Tytuł artykułu

Avoiding look-ahead in the Lanczos method and Padé approximation

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the non-normal case, it is possible to use various look-ahead strategies for computing the elements of a family of regular orthogonal polynomials. These strategies consist in jumping over non-existing and singular orthogonal polynomials by solving triangular linear systems. We show how to avoid them by using a new method called ALA (Avoiding Look-Ahead), for which we give three principal implementations. The application of ALA to Padé approximation, extrapolation methods and Lanczos method for solving systems of linear equations is discussed.
Rocznik
Tom
26
Numer
1
Strony
33-62
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-07-06
Twórcy
  • Laboratoire d'Analyse Numérique et d'Optimisation, UFR IEEA-M3
Bibliografia
  • [1] E. H. Ayachour, Avoiding the look-ahead in the Lanczos method, Publ. ANO-363, Univ. des Sciences et Technologies de Lille, 1996.
  • [2] E. H. Ayachour, Application de la biorthogonalité aux méthodes de projection, thèse, Université des Sciences et Technologies de Lille, 1998.
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  • [9] C. Brezinski and M. Redivo Zaglia, Extrapolation Methods--Theory and Practice, North-Holland, Amsterdam, 1994.
  • [10] C. Brezinski and M. Redivo Zaglia, Look-ahead in Bi-CGSTAB and other methods for linear systems, BIT 35 (1995), 169-201.
  • [11] C. Brezinski and M. Redivo Zaglia, A look-ahead strategy for the implementation of old and new extrapolation methods, Numer. Algorithms 11 (1996), 35-55.
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  • [27] P. Sonneveld, CGS: a fast Lanczos-type solver for nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. 10 (1989), 36-52.
  • [28] H. A. Van Der Vorst, Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, ibid. 13 (1992), 631-644.
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Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-zmv26i1p33bwm
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