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.
Cite this article
A.P. Zabrejko, Petr P. Zabrejko, Chebyshev Polynomial Iterations and Approximate Solutions of Linear Operator Equations. Z. Anal. Anwend. 13 (1994), no. 4, pp. 667–681DOI 10.4171/ZAA/484