Singular P-loop Array Block Aor Iteration Convergence And Monotone Matrix Convergence Theorem And Comparison Theorem Of The Double Split

Following the electronic computer invention and quick development.numerical computing has become an important method,paralled to analysis of theory and ex periment of science and engineering technique science.It is well known, many numer-ical computing questions can be attributed to how to get the solutions of the linear system of equations.In order to solve the linear system Ax=b, two methods are usu-ally adopted, that is, the direct method and the iterative method. Iterative method is widely used to solving linear systems for its less storage space and uncomplicated procedure engineering.especially presenting more superiority in large-scale numeri-cal computing,therefore,schloars have done much research on this issue (see[1-9]).Since convergence is the core issue for the iterative method, it is meaningful to study how to accelerate the rate of convergence under this circumstance. We usually make some research about the semiconvergence of a singular matrix.In order to solve linear system much faster and better,we introduce block AOR method and extrapolation iterative method.On the basis of this theory,chapter 2 works on the semiconvergence of block AOR method for singular linear systems with p-cyclic matrices.Furthermore,chapter 3 introduces the topic of double splitting for monotone matrices and obtain theorems of convergence and comparison conclusions.As is well known,Woznicki first gives this definition which had been done massive research by many scholars later on.such as Hermitian positive matrices,M-matrices,H-matrices with having gained better resultsThe follwings are the construction of this paper and the main contents of every chapter.Chapter 1. Preliminaries.This part mainly introduces the ideds of several com-monly used iterative methods and some background knowledge of the splitting of matrices.then our main research work is summiaried.In chapter 2. semiconvergence of block AOR method for singular linear systems with p-cyclic matrices. Firstly,we introduce some background knowledge of block AOR method and extrapolation iterative method.Secondly, extrapolation iterative method is appied to abtain some sufficicent conditions for the semiconvergence of the block AOR method for solving a general p-cyclic singular systems. Finally.some sufficient conditions are proved when the eigenvaluesμof the block Jacobi satisfing |μ|p=1,|μ|<1 and a numerical example is given for support.In chapter 3,convergence and comparison theorems for double splittings of ma-trices. Firstly, we introduce some background knowledge of the splitting of matri-ces. Then,we put forward a new definition of double splitting of matrices which is first defined by Woznicki and provide the definition with the second weak regualar dou-ble splitting.Moreover,we prove new convergent theorem and comparison results for two double splitting of a monotone matrix.Finally,some numerical examples mainly verify the results.