Acceleration properties of the hybrid procedure for solving linear systems

Anna Abkowicz; Claude Brezinski

Applicationes Mathematicae (1996)

  • Volume: 23, Issue: 4, page 417-432
  • ISSN: 1233-7234

Abstract

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The aim of this paper is to discuss the acceleration properties of the hybrid procedure for solving a system of linear equations. These properties are studied in a general case and in two particular cases which are illustrated by numerical examples.

How to cite

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Abkowicz, Anna, and Brezinski, Claude. "Acceleration properties of the hybrid procedure for solving linear systems." Applicationes Mathematicae 23.4 (1996): 417-432. <http://eudml.org/doc/219143>.

@article{Abkowicz1996,
abstract = {The aim of this paper is to discuss the acceleration properties of the hybrid procedure for solving a system of linear equations. These properties are studied in a general case and in two particular cases which are illustrated by numerical examples.},
author = {Abkowicz, Anna, Brezinski, Claude},
journal = {Applicationes Mathematicae},
keywords = {linear equations; acceleration; iterative methods; convergence acceleration; convergence; iterative method; linear system; hybrid procedure; numerical examples},
language = {eng},
number = {4},
pages = {417-432},
title = {Acceleration properties of the hybrid procedure for solving linear systems},
url = {http://eudml.org/doc/219143},
volume = {23},
year = {1996},
}

TY - JOUR
AU - Abkowicz, Anna
AU - Brezinski, Claude
TI - Acceleration properties of the hybrid procedure for solving linear systems
JO - Applicationes Mathematicae
PY - 1996
VL - 23
IS - 4
SP - 417
EP - 432
AB - The aim of this paper is to discuss the acceleration properties of the hybrid procedure for solving a system of linear equations. These properties are studied in a general case and in two particular cases which are illustrated by numerical examples.
LA - eng
KW - linear equations; acceleration; iterative methods; convergence acceleration; convergence; iterative method; linear system; hybrid procedure; numerical examples
UR - http://eudml.org/doc/219143
ER -

References

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  1. [1] C. Brezinski and M. Redivo Zaglia, Hybrid procedures for solving linear systems, Numer. Math. 67 (1994), 1-19. Zbl0797.65023
  2. [2] R. W. Freund, A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems, SIAM J. Sci. Statist. Comput. 14 (1993), 470-482. Zbl0781.65022
  3. [3] N. Gastinel, Procédé itératif pour la résolution numérique d'un système d'équations linéaires, C. R. Acad. Sci. Paris 246 (1958), 2571-2574. Zbl0081.34004
  4. [4] K. Jbilou, Projection-minimization methods for nonsymmetric linear systems, Linear Algebra Appl. 229 (1995), 101-125. Zbl0837.65032
  5. [5] K. Jbilou, G-orthogonal projection methods for solving linear systems, to appear. 
  6. [6] W. Schönauer, Scientific Computing on Vector Computers, North-Holland, Amsterdam, 1987. 
  7. [7] W. Schönauer, H. Müller and E. Schnepf, Numerical tests with biconjugate gradient type methods, Z. Angew. Math. Mech. 65 (1985), T400-T402. 
  8. [8] R. Weiss, Convergence behavior of generalized conjugate gradient methods, Ph.D. Thesis, University of Karlsruhe, 1990. Zbl0738.90074
  9. [9] R. Weiss, Error-minimizing Krylov subspace methods, SIAM J. Sci. Statist. Comput. 15 (1994), 511-527. Zbl0798.65048
  10. [10] R. Weiss, Properties of generalized conjugate gradient methods, Numer. Linear Algebra Appl. 1 (1994), 45-63. Zbl0816.65013
  11. [11] R. Weiss and W. Schönauer, Accelerating generalized conjugate gradient methods by smoothing, in: Iterative Methods in Linear Algebra, R. Beauwens and P. de Groen (eds.), North-Holland, Amsterdam, 1992, 283-292. Zbl0785.65045
  12. [12] L. Zhou and H. F. Walker, Residual smoothing techniques for iterative methods, SIAM J. Sci. Statist. Comput. 15 (1994), 297-312. Zbl0802.65041

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