The Superiority of a New Type of (2,2)-Step Iterative Methods Over the Related Chebyshev Method
Applied Mathematics and Computation
A new type (2,2)-step iterative method related to an optimal Chebyshev method is developed for solving real and nonsymmetric linear systems of the form Ax=b. It is an extension of the (2,2)-step iterative method introduced in [Numer. Linear Algebra Appl. 7 (2000) 169]. The superiority of the new type (2,2)-step iterative method over the optimal Chebyshev method is derived in the case where the known (2,2)-step iterative method may not improve the asymptotic rate of convergence. Two numerical examples are given to illustrate the results.
Chen, Mei-Qin, Xiezhang Li.
"The Superiority of a New Type of (2,2)-Step Iterative Methods Over the Related Chebyshev Method."
Applied Mathematics and Computation, 162 (2): 605-625.
doi: 10.1016/j.amc.2003.12.112 source: https://www.sciencedirect.com/science/article/pii/S0096300304001183?via%3Dihub