An acceleration scheme based on stationary
iterative methods is presented for solving linear system of equations. Unlike Chebyshev semi-iterative method
which requires accurate estimation of the bounds for iterative matrix
eigenvalues, we use a wide range of Chebyshev-like polynomials for
the accelerating process without estimating the bounds of the
iterative matrix. A detailed error analysis is presented and convergence rates are obtained.
Numerical experiments are carried out and comparisons with classical Jacobi and Chebyshev semi-iterative methods