Convergence And Divergence Analysis Of Preconditioned PSD Iteration Method For Solving Linear Equations

Many practical problems, such as weather forecasting, reservoir simulation, structural strength calculations, electromagnetic theory and economic analysis fi-nally come down to solve linear systems Ax=b. There are two major approaches to resolve linear systems:directive method and iterative method. Iterative method is an important method for solving large sparse matrix equations, the advantages are less storage, easy to implementation and invariant of the coefficient matrix.The key measurement of iterative method is its convergence property, for ex-ample convergence rate. Generally speaking, the convergence properties are closely related with the coefficient matrix. So something can be done of the coefficient ma-trix to improve the speed of convergence of iterative methods, one widely used such technique is preconditions.Convergence and divergence properties of preconditioned PSD iterative method for irreducible L-matrix are studied in this thesis. The main contents can be divided into three part:The first part introduces the background of iterative method and the state of art of preconditioned iterative method.The second part presents the basic iterative method. the PSD iterative method and some special iterative method, some definitions and lemmas are also given in this part.The third part is the main body of this thesis. i.e. the convergence’and diver-gence analysis of precondition PSD iterative method for irreducible L-matrix. Four types of preconditions methods are studied based on reference [1]. The convergence and divergence comparison theorem are derived in third part.The forth part gives some numerical examples.and illustrate the correctness and effective of the proposed method.