Quasi-Chebyshev accelerated iteration methods based on optimization for linear systems

In this paper, we present a quasi-Chebyshev accelerated iteration method for solving a system of linear equations. Compared with the Chebyshev semi-iterative method, the main difference is that the parameter ωω is not obtained by a Chebyshev polynomial but by optimization models. We prove that the quasi-Chebyshev accelerated iteration method is unconditionally convergent if the original iteration method is convergent, and also discuss the convergence rate. Finally, three numerical examples indicate that our method is more efficient than the Chebyshev semi-iterative method.