An Acceleration Method for Stationary Iterative Solution to Linear System of Equations (Advances in Applied Mathematics and Mechanics, 2012)
An acceleration scheme based on stationary iterative methods is presented for solving linear system of equations. Unlike Chebyshev semi-iterative methodwhich requires accurate estimation of the bounds for iterative matrixeigenvalues, we use a wide range of Chebyshev-like polynomials forthe accelerating process without estimating the bounds of theiterative 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 methodsare provided.