亚正定四元数矩阵方程的NPSS迭代及外推  

On NPSS Iteration and Extrapolation Method of the Sub-Positive Definite Quaternion Matrix Equation

作　　者：张姗姗 黄敬频[1] 熊昊 ZHANG Shanshan;HUANG Jingpin;XIONG Hao(School of Mathematics and Physics,Guangxi University for Nationalities,Nanni ng 530006,China)

机构地区：[1]广西民族大学数学与物理学院,南宁530006

出　　处：《重庆师范大学学报（自然科学版）》2022年第2期96-102,共7页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11661011);广西民族大学研究生创新项目(No.gxun-chxps202071)。

摘　　要：【目的】研究四元数体上亚正定矩阵方程AX=B的分裂迭代求解问题。【方法】利用四元数正规矩阵和亚正定矩阵的自共轭分支与斜自共轭分支,建立两种新的NPSS分裂迭代,并引入参数对它们统一加速处理。【结果】获得外推NPSS迭代(简称ENPSS),证明了ENPSS迭代收敛于原方程组的唯一解,同时给出迭代收敛因子的一个上界及拟最优参数估计式。【结论】把复矩阵方程的分裂求解问题推广到四元数体讨论,并构建出新的ENPSS迭代,数值算例验证了所给迭代的有效及可行性。[Purposes]The present work proposed the problem of splitting iteration for the Sub-positive Definite Matrix equation AX=B over the quaternion field. [Methods] By using the self-conjugate and skew-self-conjugate splitting of quaternion normal matrix and sub-positive definite matrix, two new NPSS splitting iterations are established, and parameters are introduced to speed them up. [Findings] The extrapolation NPSS iteration(ENPSS) is obtained. It is proved that the ENPSS iteration converges to the unique solution of the original equations. At the same time, an upper bound of the iterative convergence factor and the quasi optimal parameter estimation are given. [Conclusions] The splitting problem of complex matrix equation is extended to the quaternion field, and a new ENPSS iteration is constructed. Numerical examples show the effectiveness and feasibility of the proposed iteration.

关 键 词：四元数体 亚正定矩阵 交替迭代 NPSS迭代 ENPSS迭代 

分 类 号：O241.6[理学—计算数学]