一类复对称线性系统的参数化PMHSS迭代方法

发布时间：2019-04-11 10:08

【摘要】：基于预处理修正的Hermitian和skew-Heimitian分裂(PMHSS)迭代方法和交替方向的PMHSS(ADPMHSS)迭代方法的思想,本文提出了一种新的迭代方法来求解一类复对称线性系统,即参数化PMHSS(P2MHSS)迭代方法.在本文中,我们不仅从预处理矩阵的角度给出了 P2MHSS迭代方法的参数选取方法和计算公式,还分析了该方法的收敛性质,并证明了其在一定条件下对任意的初始向量都会收敛到该线性系统的精确解.最后,我们用数值算例验证了 P2MHSS迭代方法的可行性和有效性.
[Abstract]:In this paper, a new iterative method is proposed to solve a class of complex symmetric linear systems, i.e., the parametric PMHSS (P2MHSS) iterative method, based on the pre-processing modified Hermitian and the skew-Heimitian splitting (PMHSS) iterative method and the alternating direction PMHSS (ADPMHSS) iterative method. In this paper, we not only give the parameter selection method and calculation formula of the P2MHSS iterative method from the angle of the pre-processing matrix, and also analyze the convergence property of the method, and prove that any initial vector will converge to the exact solution of the linear system under certain conditions. Finally, we use a numerical example to verify the feasibility and effectiveness of the P2MHSS iterative method.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.6

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