Methods For Some Structured Singular Linear Systems

With the rapid development of modern science and technology,large-scale and complicated calculation has become a stumbling block for all kinds of scientific computing and engineering technology.These problems are reduced to solve large sparse linear systems xb A(28).This paper mainly studies several iterative algorithms to solve singular linear systems and the research content is mainly divided into the following four parts:First,the Generalized Minimal Residual with right pretreatment(GMRES)method is used to solve singular linear systems xb A(28).In addition,we further discuss the characteristic of proper splitting and some classical results of the time-invariant iterative method are generalized.Second,the two-step parameterized iteration method(TSP)is generalized to solve singular complex symmetric linear systems.And the validity of TSP iterative method is verified in theory.Third,the an efficient parameterized single-step preconditioned variant of HSS iterative method(PSPHSS)is generalized to solvesingular complex symmetric linear systems.When the coefficient matrix condition is weakened and the preprocessing matrix is type I or type II,we analyz the PSPHSS iterative method whose semi-convergence property and the optimal parameter of minimizing the quasi-spectral radius.Finally,the validity of PSPHSS iterative method is verified in theory.Fourth,the validity of the algorithm is verified by numerical experiments.