A Generalized Splitting Iterative Method For The Discrete Dynamic Linear System

In many fields of modern scientific computing and engineering technology,such as fluid mechanics,computational electromagnetics,elastic dynamics,many system problems finally can be transformed into the solution of large sparse linear system equations.Thus,how to solve the large spares linear system effectively is particularly important in computational mathematics.In recent years,with the development of preconditioning technology,many experts and scholars have proposed a series of methods based on Hermitian and skew-Hermitian splitting iterative method to solve large sparse linear system equations,and made great progress in this field.In accordance with above,in this study,the main research direction is the problem of solving the dynamic linear system equation by using the idea of HSS series iterative algorithm,and proposed the corresponding improved optimization algorithm.The main research contents of this paper are as follows:Firstly,Introducing the history of solving the dynamic linear system and transforming it into the form of large spare linear system equation.Secondly,Deciding to choose the complex-symmetric and skew-Hermitian splitting iterative method to solve this problem by thinking of the series of the HSS iterative algorithms.Thirdly,Improving the algorithm by introducing two different parameters and making it more flexible.Both theoretical deduction and numerical examples show that GCSS iterative method is superior to CSS iterative method when dealing with the same form system equations in terms of the number of iterations and the computing time.What's more,GCSS iterative method can solve the dynamic linear system problems more effectively.Finally,Speeding up the algorithm by the Krylov subspace method in practical application,and both theoretical and numerical results show the effectiveness of the improved algorithm.