This article is cited in 1 paper

Refinement of convergence conditions of the Chebyshev method

M. I. Nechepurenko

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences

Abstract: The iterative Chebyshev method of an approximate solution of equations of the form $F(x)=0$ in Banach spaces is studied, assuming that $F''$ satisfies the Lipschitz condition. Accurate (attainable) estimates of the domains of existence and uniqueness of solution, non-refinable conditions of existence and convergence of the Chebyshev method as well as asymptotic estimates of the rate of convergence have been obtained.

Key words: equations in Banach spaces, iterative Chebyshev method, accurate estimates, domains of existence and uniqueness.

UDC: 517.988.8

Received: 31.03.2003
Revised: 25.12.2003

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