Nonnegative Double Division Of Research

With the development of natural science and engineering technology science, numerical value computing has become an important method,paralleled to theory analysis and scientific experiment. It is well known, many numerical value com-puting questions can be attributed to how to get the solutions of the linear sys-tem of equations.When solving the linear system Ax=b, two methods are usually adopted, that is, the direct method and the iterative method. The direct solving method is convenient for the linear system with not very high order. The accurate answer will be produced through several limited operations if there is no rounding errors.Iterative method is widely used to solving linear systems for its less storage space and uncomplicated procedure engineering, especially presenting more superi-orly in large-scale numerical computing.The iterative method is a commonly used method for solving linear equa-tions.The splitting method which is studied in this paper is a specific application of the iterative method. The splitting of the coefficient matrix A=M-N,where M is nonsingular,is called a single splitting of A. Recently.some cnvergence and comparison theorems for single splittings or multisplittings of matrices have been arisen in some papers and books. The double splitting of A was put forward by Woznicki in1993. Then some papers on the double splittings have appeared.Shen and Huang presented convergence and comparison theorems for double splittings of monotone matrices and of Hermitian positive definite matrices. Chapter II of this paper is devoted to giving nonnegative double splitting theories of the coefficient matrix A,which is more general. Positive cones and convergence conditions for iterative methods based on nonnegative double splittings are presented in Chapter III.