A New Pre-Conditioned Iterative Method

With the rapid development of modern science and technology, solving equations has become an indispensable tool of treating various mathematical problems in science and technology. In order to fast and accurately for solve large sparse matrix equations,iterative method is undoubtedly the most effective way. The iterative method is good or bad depends directly on the spectral radius of iteration matrix. Only the spectral radius of the selected iterative matrix is less than one,can the iterative method maintain converging. In the practice, in order to accelerate the convergence rate of iteration , preconditioning of the coefficient matrix and making the treated iteration matrix has a good convergence is particularly important.The paper mainly introduces P = I + C_α+F~βas a preconditioned matrix .It proves that when the coefficient matrix A is an H matrix, the preconditioned matrix of A is still an H- matrix in given conditions .The paper also discusses the comparison theorem of the classic AOR method with the preconditioned AOR method which is for the coefficient matrix A when it is an L-matrix satisfying certain conditions .This structure and main contents of the paper are as follows: Chapter I, introduction , mainly discusses several comment iterative methods and the development of preconditioning .Chapter II, preliminary, mainly lists the mathematical definitions and lemmas used in this article.Chapter III, introduces as P = I + C_α+F~βa preconditioned matrix. It proves that when the coefficient matrix is an H-matrix the preconditioned matrix of it is still an H-matrix.Chapter IV , discusses the comparison theorem of the classical AOR iterative method with the preconditioned AOR method under the premise that the coefficient matrix is An L-matrix. At the end , numerical example is given.