A new preconditioned Richardson iterative method

Abstract

In this paper, we propose a new iterative technique for solving an operator equation $Ax=y$ based on the Richardson iterative method. Then, by using the Chebyshev polynomials, we modify the proposed method to accelerate the convergence rate. Also, we present the results of some numerical experiments that demonstrate the efficiency and effectiveness of the proposed methods compared to the existing, state-of-the-art methods.

Keywords

• iterative method
• Richardson iteration
• convergence rate
• Chebyshev polynomials