Convergence of Chebyshev semi-iterative methods

摘要

In this paper we prove a sufficient condition for convergence of Chebyshev semi-iterative (SI) methods applied to the numerical resolution of algebraic linear systems. The convergence condition depends on the bounds on the eigenvalues of a particular matrix; the matrix is associated with the well-known Chebyshev SI method defined by Varga [3], or equivalently, the Chebyshev extrapolation method by Young [5].