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Zeitschrift für Analysis und ihre Anwendungen


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Volume 13, Issue 4, 1994, pp. 667–681
DOI: 10.4171/ZAA/484

Published online: 1994-12-31

Chebyshev Polynomial Iterations and Approximate Solutions of Linear Operator Equations

A.P. Zabrejko[1] and Petr P. Zabrejko[2]

(1) Peoples’ Friendship University of Russia, Moscow, Russian Federation
(2) Belgos University, Minsk, Belarus

An iteration scheme for the approximate solution of a linear operator equation in a Banach space is discussed from the viewpoint of Chebyshev polynomials. The optimal rate of convergence is described by numerical characteristics which are similar to (but different from) the classical Chebyshev constants. The abstract results are illustrated by some examples which frequently arise in applications.

Keywords: Polynomial iterations, Chebyshev polynomials, Chebyshev characteristics

Zabrejko A.P., Zabrejko Petr: Chebyshev Polynomial Iterations and Approximate Solutions of Linear Operator Equations. Z. Anal. Anwend. 13 (1994), 667-681. doi: 10.4171/ZAA/484