Numerical Analysis
A superconvergent projection method for nonlinear compact operator equations
Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 215-218.

We propose a method based on projections for approximating fixed points of a compact nonlinear operator. Under the same assumptions as in the Galerkin method, the proposed solution is shown to converge faster than the Galerkin solution.

Nous proposons une méthode, basée sur une projection, pour approcher les points fixes localement uniques d'un opérateur compact. Cette méthode présente un avantage par rapport aux méthodes de Galerkin et de Galerkin itérée étudiées par K.E. Atkinson and F.A. Potra : on n'a pas besoin de conditions supplémentaires pour obtenir la superconvergence de la solution approchée vers la solution exacte.

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Published online:
DOI: 10.1016/j.crma.2005.11.011
Grammont, Laurence 1; Kulkarni, Rekha 2

1 Laboratoire de mathématiques de l'université de Saint-Étienne, 23, rue du Dr. Paul Michelon, 42023 Saint Étienne cedex 2, France
2 Department of Mathematics, Indian Institute of Technology, Powai, Mumbai 400076, India
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Grammont, Laurence; Kulkarni, Rekha. A superconvergent projection method for nonlinear compact operator equations. Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 215-218. doi : 10.1016/j.crma.2005.11.011. http://www.numdam.org/articles/10.1016/j.crma.2005.11.011/

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[2] Atkinson, K.E.; Potra, F.A. Projection and iterated projection methods for nonlinear integral equations, SIAM J. Numer. Anal., Volume 24 (1987) no. 6, pp. 1352-1373

[3] Krasnosel'skii, M.A.; Vainikko, G.M.; Zabreiko, P.P.; Rutitskii, Y.; Stetsenko, V. Approximate Solution of Operator Equation, P. Noordhoff, Groningen, 1972

[4] Krasnosel'skii, M.A.; Zabreiko, P.P. Geometrical Methods of Nonlinear Analysis, Springer-Verlag, Berlin, 1984

[5] Kulkarni, R.P. A superconvergence result for solutions of compact operator equations, Bull. Austral. Math. Soc., Volume 68 (2003), pp. 517-528

[6] Kulkarni, R.P. A new superconvergent projection method for approximate solutions of eigenvalue problems, Numer. Funct. Anal. Optim., Volume 24 (2003), pp. 75-84

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