A new preconditioned Richardson iterative method

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 effectivenessof the proposed methods compared to the existing, state-of-the-art methods.