求解多重线性系统的预条件张量分裂Gauss-Seidel迭代法  

The Preconditioned Gauss-Seidel Iterative Method by Tensor Spliitting for Solving Multilinear Systems

作　　者：种园园 吕长青 CHONG Yuanuan;L Changqing(School of Mathematics and Statistics,Zaozhuang University,Zaozhuang 277160,China)

机构地区：[1]枣庄学院数学与统计学院,山东枣庄277160

出　　处：《枣庄学院学报》2023年第5期39-46,共8页Journal of Zaozhuang University

基　　金：山东省自然科学基金资助(2R2021MA094)。

摘　　要：为了解决建立在强M-张量上的多重线性系统的预处理Gauss-Seidel迭代法,提出一个新的预条件子I+S'α,给出张量分裂,提出3种不同的Gauss-Seidel分裂方式,形成预处理迭代张量,并证明它们是收敛的。比较基于不同分裂形式的Gauss-Seidel迭代收敛速度,通过数值算例验证了所给算法是可行有效的。This paper is devoted to solve the multi-liner systems by the preconditioned Gauss-Seidel iterative methods based on strong M-tensors.We consider a new preconditioner I+Sα',and give three different Gauss-Seidel splitting forms,then prove that their convergence.The convergence rates of Gauss-Seidel iterations with different splitting forms are compared.Several numerical examples are given to verify that the proposed algorithm is feasible and effective.

关 键 词：强M-张量 张量分裂 多重线性系统 预条件子 预处理Gauss-Seidel 

分 类 号：O241.7[理学—计算数学]