Comptes Rendus
no. 12
Numerical Analysis
On some matrix extrapolation methods
[Sur des nouvelles méthodes d'extrapolation matricielle]

Présenté par : Philippe G. Ciarlet

Khalide Jbilou1 ; Abderrahim Messaoudi2 ; Khalid Tabaa3
1 Université du littoral, côte d'opale, bâtiment H. Poincaré, 50, rue F. Buisson, 62280 Calais cedex, France
2 École normale supérieure Takaddoum, département de mathématiques, B.P. 5118, avenue Oued-Akreuch, Takaddoum, Rabat, Morocco
3 Département de mathématiques, faculté des sciences de Rabat, Agdal, Rabat, Morocco
Comptes Rendus. Mathématique, Volume 341 (2005) no. 12, pp. 781-786.

Dans cette Note, nous introduisons de nouvelles méthodes d'extrapolation matricielle comme généralisation de certaines méthodes d'extrapolation vectorielle. Les approximations obtenues sont données sous forme de complément de Schur. Ces méthodes seront ensuite appliquées à des suites matricielles générées linéairement et des résultas théoriques sont proposés.

In the present Note we introduce new matrix extrapolation methods as a generalization of well known vector extrapolation methods. We give expressions of the obtained approximation via the Schur complement. We apply these methods to linearly generated sequences and give some theoretical results.

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DOI : 10.1016/j.crma.2005.10.019
Khalide Jbilou 1 ; Abderrahim Messaoudi 2 ; Khalid Tabaa 3

1 Université du littoral, côte d'opale, bâtiment H. Poincaré, 50, rue F. Buisson, 62280 Calais cedex, France
2 École normale supérieure Takaddoum, département de mathématiques, B.P. 5118, avenue Oued-Akreuch, Takaddoum, Rabat, Morocco
3 Département de mathématiques, faculté des sciences de Rabat, Agdal, Rabat, Morocco 
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Khalide Jbilou; Abderrahim Messaoudi; Khalid Tabaa. On some matrix extrapolation methods. Comptes Rendus. Mathématique, Volume 341 (2005) no. 12, pp. 781-786. doi : 10.1016/j.crma.2005.10.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.10.019/

[1] C. Brezinski Généralisation de la transformation de Shanks, de la table de la Table de Padé et l'epsilon-algorithm, Calcolo, Volume 12 (1975), pp. 317-360

[2] C. Brezinski The block Lanczos and Vorobyev methods, C. R. Acad. Sci. Paris, Sér. I, Volume 331 (2000), pp. 137-142

[3] C. Brezinski Block descent methods and hybrid procedures for linear systems, Numer. Algorithms, Volume 29 (2002), pp. 21-32

[4] C. Brezinski; M. Redivo Zaglia Extrapolation Methods. Theory and Practice, North-Holland, Amsterdam, 1991

[5] C. Brezinski; M. Redivo Zaglia Vector and matrix sequence transformations based on biorthogonality, Appl. Numer. Math., Volume 21 (1996), pp. 353-373

[6] C. Brezinski; M. Redivo Zaglia A Schur complement approach to a general extrapolation algorithm, Linear Algebra Appl., Volume 368 (2003), pp. 279-301

[7] S. Cabay; L.W. Jackson A polynomial extrapolation method for finding limits and antilimits for vector sequences, SIAM J. Numer. Anal., Volume 13 (1976), pp. 734-752

[8] R.P. Eddy Extrapolation to the limit of a vector sequence (P.C.C. Wang, ed.), Information Linkage Between Applied Mathematics and Industry, Academic Press, New York, 1979, pp. 387-396

[9] K. Jbilou; H. Sadok Analysis of some vector extrapolation methods for linear systems, Numer. Math., Volume 70 (1995), pp. 73-89

[10] K. Jbilou; H. Sadok LU-implementation of the modified minimal polynomial extrapolation method, IMA J. Numer. Anal., Volume 19 (1999), pp. 549-561

[11] M. Mes`ina Convergence acceleration for the iterative solution of x=Ax+f, Comput. Methods Appl. Mech. Engrg., Volume 10 (1977) no. 2, pp. 165-173

[12] B.P. Pugatchev Acceleration of the convergence of iterative processes and a method for solving systems of nonlinear equations, USSR Comput. Math. Math. Phys., Volume 17 (1978), pp. 199-207

[13] Y. Saad Iterative Methods for Sparse Linear Systems, PWS Press, New York, 1995

[14] A. Sidi Convergence and stability of minimal polynomial and reduced rank extrapolation algorithms, SIAM J. Numer. Anal., Volume 23 (1986), pp. 197-209

[15] A. Sidi; W.F. Ford; D.A. Smith Acceleration of convergence of vector sequences, SIAM J. Numer. Anal., Volume 23 (1986), pp. 178-196

[16] P. Wynn Acceleration technique for iterated vector and matrix problems, Math. Comp., Volume 16 (1962), pp. 301-322

[17] F.-Z. Zhang The Schur Complement and its Applications, Springer, New York, 2005

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