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Abstract: A breakdown (due to a division by zero) can arise in the algorithms for implementing Lanczos' method because of the non--existence of some formal orthogonal polynomials or because the recurrence relationship used is not appropriate. Such a breakdown can be avoided by jumping over the polynomials involved. This strategy was already used in some algorithms such as the MRZ and its variants. In this paper, we propose new implementations of the recurrence relations of these algorithms which only... (Update)
Context of citations to this paper: More
.... such as Lanczos Orthores, Lanczos Orthodir, or the algorithms given in [8] This is also possible in the algorithms presented in [5, 6, 7] for curing breakdowns and near breakdowns in Lanczos process since they directly derive from the theory of FOP. Changing the...
.... x 19] Recently, a number of further look ahead like algorithms for Lanczostype solvers have been proposed by Ayachour [1] Brezinski et al. [7], Graves Morris Applied Mathematics, ETH Zurich, ETH Zentrum HG, CH 8092 Zurich, Switzerland (mhg sam.math.ethz.ch) Formerly at...
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On the choice of the auxiliary vectors in Lanczos'.. - Brezinski, Redivo-Zaglia (1999) (Correct)
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1.3: The matrix and polynomial approaches to Lanczos-type.. - Brezinski.. (2001) (Correct)
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3: Look-ahead in Bi-CGSTAB and other product methods for linear systems - Brezinski, Redivo-Zaglia - 1995
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BibTeX entry: (Update)
C. Brezinski, M. Redivo--Zaglia, H. Sadok, New look--ahead Lanczos--type algorithms for linear systems, Numer. Math., to appear. 261--284. http://citeseer.ist.psu.edu/brezinski97new.html More
@article{ brezinski99new,
author = "C. Brezinski and M. Redivo Zaglia and H. Sadok",
title = "New look-ahead {Lanczos}-type algorithms for linear systems",
journal = "Numerische Mathematik",
volume = "83",
number = "1",
month = "????",
pages = "53--85",
year = "1999",
url = "citeseer.ist.psu.edu/brezinski97new.html" }
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86 A look--ahead Lanczos algorithm for unsymmetric matrices (context) - Parlett, Taylor et al. - 1985
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49 Templates for the Solution of Linear Systems: Building block.. (context) - Barret, Berry - 1994
46 Pad'e--Type Approximation and General Orthogonal Polynomials (context) - Brezinski - 1980
36 Analysis of the Look--Ahead Lanczos Algorithm (context) - Taylor - 1982
34 an iterative method for solving sparse sets of simultaneous .. (context) - Vinsome - 1976
31 Avoiding breakdown and near--breakdown in Lanczos type algor.. (context) - Brezinski, Redivo--Zaglia et al. - 1991
31 Avoiding breakdown and near-- breakdown in Lanczos type algo.. (context) - Brezinski, Redivo--Zaglia et al. - 1992
27 A breakdown--free Lanczos type algorithm for solving linear .. (context) - Brezinski, Redivo--Zaglia et al. - 1992
25 The unsymmetric Lanczos algorithms and their relations to Pa.. - Gutknecht - 1990
16 Nonsymmetric Lanczos and finding orthogonal polynomials asso.. (context) - Boley, Elhay et al. - 1991
14 the simplification of generalized conjugate gradient methods.. (context) - Jea, Young - 1983
13 A composite step bi--conjugate gradient algorithm for solvin.. (context) - Bank, Chan - 1994
13 Orthogonal polynomials: variable--signed Weight Functions (context) - Struble - 1963
11 Breakdowns in the computation of orthogonal polynomials - Brezinski, Redivo--Zaglia - 1994
11 A breakdown--free variation of the nonsymmetric Lanczos algo.. (context) - Ye - 1994
11 A new presentation of orthogonal polynomials with applicatio.. (context) - Brezinski, Redivo--Zaglia - 1991
10 Lanczos type methods for solving systems of linear equations (context) - Brezinski, Sadok - 1993
10 A composite step conjugate gradients squared algorithm for s.. (context) - Chan, Szeto - 1994
10 An analysis of the composite step bi--conjugate gradient alg.. (context) - Bank, Chan - 1993
10 Polynomes Orthogonaux Formels (context) - Draux - 1983
9 New implementations of Lanczos method (context) - Baheux - 1995
6 Breakdowns in the implementation of the L'anczos method for .. - Brezinski, Redivo--Zaglia et al. - 1997
5 Lanczos maximal algorithm for unsymmetric eigenvalue problem.. (context) - Khelifi - 1991
5 Generating conjugate directions for arbitrary matrices by ma.. (context) - us - 1991
4 An adaptative block Lanczos algorithm (context) - Ye - 1996
3 Two conjugate-gradient-type methods for unsymmetric linear e.. (context) - Saunders, Simon et al. - 1988
2 A linear system solver based on a modified Krylov subspace m.. (context) - Tong, Ye - 1996
2 Look--ahead block--CG algorithms (context) - Broyden
2 Universit'e des Sciences et Technologies de Lille (context) - Ayachour
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