Practical convergent splittings and acceleration methods for non-Hermitian positive definite linear systems

Abstract

We present two practical convergent splittings for solving a non-Hermitian positive definite system. By these new splittings and optimization models, we derive three new improved Chebyshev semi-iterative methods and discuss convergence of these methods. Finally, the numerical examples show that the acceleration methods can reduce evidently the amount of work in computation.