A Proposal of Variants of BiCGSafe Method for Solving Linear Systems in Realistic Problems

摘要

We consider on efficient and stable solution for linear systems by product-type iterative methods. By means of improvement on ordering of Lanczos and stability polynomials which construct algorithm of product-type BiCG method, we derive new algorithm based on BiCGSafe method with safety convergence. We will apply the proposed BiCGSafe method to solve linear systems which appeared in a variety of realistic problems. Through numerical experiments, we will make clear that the proposed variants of BiCGSafe method have an excellent convergence rate.