On choices of iteration parameter in HSS method

The HSS iteration method is effective to solve non-Hermitian positive definite linear systems, but the choice of its optimal parameter is a difficult and challenging problem in theoretical analysis and practical computations. In this paper, we obtain an accurate estimate to the optimal parameter of the HSS iteration method by adopting a reasonable and simple optimization principle. Numerical experiments show that this principle is feasible to produce an accurate estimate to the optimal parameter of the HSS iteration method.