Abstract
In this paper, several procedures for accelerating the convergence of an iterative method for solving a system of linear equations are proposed. They are based on projections and are closely related to the corresponding iterative projection methods for linear systems.
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References
J. Barzilai and J.M. Borwein, Two-point step size gradient methods, IMA J. Numer. Anal. 8 (1988) 141–148.
C. Brezinski, Variations on Richardson's method and acceleration, in: Numerical Analysis. A Numerical Analysis Conf. in Honor of Jean Meinguet, Bull. Soc. Math. Belg. (1996) pp. 33–44.
C. Brezinski, Projection Methods for Systems of Equations (North-Holland, Amsterdam, 1997).
C. Brezinski, Projection methods for linear systems, J. Comput. Appl. Math. 77 (1997) 35–51.
C. Brezinski, Vector sequence transformations: methodology and applications to linear systems, J. Comput. Appl. Math. 98 (1998) 149–175.
C. Brezinski, Multiparameter descent methods, Linear Algebra Appl. 296 (1999) 113–142.
C. Brezinski and J.P. Chehab, Nonlinear hybrid procedures and fixed point iterations, Numer. Funct. Anal. Optim. 19 (1998) 465–487.
C. Brezinski and J.P. Chehab, Multiparameter iterative schemes for the solution of systems of linear and nonlinear equations, SIAM J. Sci. Comput. 20 (1999) 2140–2159.
C. Brezinski and M. Redivo Zaglia, Extrapolation Methods. Theory and Practice (North-Holland, Amsterdam, 1991).
C. Brezinski and M. Redivo Zaglia, Vector and matrix sequence transformations based on biorthogonality, Appl. Numer. Math. 21 (1996) 353–373.
N. Gastinel, Procédé itératif pour la résolution numérique d'un système d'équations linéaires, C. R. Acad. Sci. Paris 246 (1958) 2571–2574.
N. Gastinel, Surdécomposition de normes générales et procédés itératifs, Numer. Math. 5 (1963) 142–151.
N.J. Higham, The test matrix toolbox for MATLAB (Version 3.0), Numerical Analysis Report 276, Department of Mathematics, The University of Manchester (1995).
A.S. Householder, The Theory of Matrices in Numerical Analysis (Blaisdell, New York, 1964).
A.S. Householder and F.L. Bauer, On certain iterative methods for solving linear systems, Numer. Math. 2 (1960) 55–59.
K. Jbilou, A general projection algorithm for solving systems of linear equations, Numer. Algorithms 4 (1993) 361–377.
S. Kaczmarz, Angenäherte Auflösung von Systemen linearer Gleichungen, Bull. Acad. Sci. Polon. A 35 (1937) 355–357.
R.S. Varga, Matrix Iterative Analysis, 2nd ed. (Springer, Berlin, 2000).
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Brezinski, C. Acceleration procedures for matrix iterative methods. Numerical Algorithms 25, 63–73 (2000). https://doi.org/10.1023/A:1016613208163
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DOI: https://doi.org/10.1023/A:1016613208163