关于H矩阵的GSAOR多重分裂方法的收敛性-应用数学专业论文.docx

扬州大学硕士论文 扬州大学硕士论文 2 关键词：收敛性，GSAOR多重分裂迭代方法，两步多重分裂迭代方法，H一矩阵，M一矩阵 孙霞：关于H一矩阵的GSAOR多重分裂方法的收敛性 孙霞：关于H一矩阵的GSAOR多重分裂方法的收敛性 3 一 Abstract When undergoing numerical simulation to many practical problems in natural science and social science，People will eventually attribute these problems to one or some large sparse matrix of linear equations，such as structural designation，calculation in numerical weather forecasting and petroleum exploration，etc．they are always used to use differential or partial differential equations as the mathematical model，however,these computing field are hign—dimension and wide-range，these pattens may probably irregular,which bring many difficulties to the calculation． With The parallel multisplitting iterative method for solving the large linear system of equations was introduced by O’Leary and White in 1 985[1]．From then on，this iterative method has been further studied by plenty of scholars．In the past few years，many researchers have developed the multisplitting iterations for solving the larger sparse linear systems．But the attention was mai nly paid to the H．matrix、M—matrix and the symmetric positive matrix(see[2-1 l】)，and only a few attention was studied on the convergence，semi—convergence of the parallel multisplitting iterative method for solving the singular linear system(see[1 2—1 6】)． In this paper,we further studied a new parallel multisplitting iterative method for solving the large linear system(GSAOR method)，and the attention was mainly paid to the method’S convergence under the H—matrix、M—matrix condition． The arrangement of this paper is as follows． 扬州大学硕士论文 扬州大学硕士论文 4 In Chapter 1，the development of the multisplitting iterative method for solving the linear system in the past few years is simply introduced． In Chapter 2，we give the definition of the multisplitting iterative method、 GSAOR method，and some basic definitions，lemmas and SO on are reviewed，and we present two methods，what are the multisplitting keration algorithm and the