Product-type Triangular Splitting Iteration Methods For Complex Linear Systems

In this master dissertation, we introduce a product-type triangular splitting iteration method(PTS) for complex linear systems. We study the convergence of the product-type triangular splitting iteration method for complex positive definite linear systems, as well as spectrum distribution of the preconditioned matrix with respect to the preconditioner induced from the product-type triangular splitting. And we prove its covergence under suitable restrictions on the iteration parameters. Furthermore,the quasi-optimal choices of the iteration parameters are also presented. By specially choosing the values of the iteration parameters, we obtain a few of the existing iteration methods in the literature. Numerical results show that the product-type triangular splitting iteration methods are effective for solving complex linear systems.