A New Judgement And Application Of H Matrix And The Convergence Condition Of AOR Iterative Method

Abstract: This paper mainly discusses a new judgement and application of H matrix and the convergence condition of AOR iterative method .As we all know, in the discussion of the linear systems, the coefficient matrix of the linear systems is usually assumed to be H matrix. There really exist many H matrices in practice. In 1976, people did much research on iterative methods of JOR, SOR and AOR.They found that the convergence of these iterative methods were closely related to H matrices ,That is,if the discussed matrix is H matrix, the iterative matrices L_r,w(G),S_r,w(G) are allconverged. Thus, when we discuss the convergence of iterative methods, it is very important to make a quick and accurate judgement on whether a matrix is H matrix or not. On the basis of this theory, the author have done much research work and offered the judgement about a new H matrix. This method is only related to elements of given matrix itself. It's very convenient and feasible. The author applies this method to theestimation of matrix norm and gets a new estimation formula ||M^-1 N||_∞ , whichbroadens the range of its application. On the basis of the summary of existing convergence condition, the author have mainly discussed the situation that the eigenvalues of Jacobi are complex numbers, and offered a convergence condition ,which have the convergent range of AOR iterative method.The Main part of this paper includes 4 chapters. The first chapter is prelude, which mainly discusses some judgement of H matrices, estimation of matrix norm and the development in recent years. The second chapter is a major part, which mainly discusses the new judgement and application of H matrices. The third chapter is application, which mainly discusses the application of the judgement and the estimation norms of H matrices. The forth chapter is also a major part, which discusses the convergent range of AOR iterative method when the eigenvalues of Jacobi are complex numbers. The details are as following:In the second part, the author firstly studies the judgement about H matrix from the literature and the explorations which the experts have done on the judgement of H matrix in recent years. The author offers a new judgement about H matrix. This method is only related to the element of existing matrix itself. Meanwhile, managed...