基于不完全正交的WIGMRES(m)算法  

WIGMRES(m)Algorithm Based on Incomplete Orthogonality

作　　者：于春肖[1] 井丁卉 杨艳芳 YU Chunxiao;JING Dinghui;YANG Yanfang(College of Science, Yanshan University, Qinhuangdao 066004, China)

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《郑州大学学报（理学版）》2021年第4期109-114,共6页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金项目(11301459);河北省自然科学基金项目(A2017203100)。

摘　　要：为提高大型线性方程组的求解速度,在WGMRES(m)算法的基础上,利用不完全正交的加权Arnoldi过程,提出了截断型变参数的WIGMRES(m)算法,并验证了该算法的收敛性。最后通过数值算例分析截断指标对计算精度和计算效率的影响,表明WIGMRES(m)算法在保证精度的前提下,大大减少了迭代次数,为实际工程的求解提供了新方法。In order to improve the solving speed of large linear equations,on the basis of WGMRES(m)algorithm,with the incomplete orthogonal weighted Arnoldi process,a truncated variable parameter WIGMRES(m)algorithm was proposed and its convergence was verified.The numerical examples were used to analyze the influence of the truncation index on the calculation accuracy and calculation efficiency.It showed that the WIGMRES(m)algorithm greatly reduced the number of iterations under the premise of ensuring accuracy,and provided a new method for practical engineering solutions.

关 键 词：WIGMRES(m)算法 不完全正交 截断型 

分 类 号：O241.6[理学—计算数学]