Modified frame algorithm and its convergence acceleration by Chebyshev method

The aim of this paper is to improve the convergence rate of frame algorithm based on Richardson iteration and Chebyshev methods. Based on Richardson iteration method, we first square the existing convergence rate of frame algorithm which in turn the number of iterations would be bisected and increased speed of convergence is achieved. Afterward, by using Chebyshev polynomials, we improve this speed too. The importance of these methods is better understood when using frame has ill conditional number (The ratio of the upper bound to the lower bound).