华东师范大学学报（自然科学版） ›› 2022, Vol. 2022 ›› Issue (4): 1-12.doi: 10.3969/j.issn.1000-5641.2022.04.001

• 数学 •    下一篇

解实正定线性方程组的交替方向迭代法新格式

征道生()   

  1. 华东师范大学 数学科学学院, 上海　200241
  • 收稿日期:2021-01-27 出版日期:2022-07-25 发布日期:2022-07-19
  • 作者简介:征道生，男，教授，研究方向为数值代数与矩阵论. E-mail: dszheng@math.ecnu.edu.cn

New form of the alternating direction iteration scheme for real positive definite linear systems

Daosheng ZHENG()   

  1. School of Mathematical Sciences, East China Normal University, Shanghai　200241, China
  • Received:2021-01-27 Online:2022-07-25 Published:2022-07-19

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摘要：

在许多适用于解实正定方程组的交替方向迭代法(Alternating Direction Iteration, ADI)的格式中, 要求诸方向矩阵之间满足乘法可交换条件. 这虽然可提高格式的效率, 却也限制了ADI的应用范围. 本文提出了一些修改的ADI格式(Revised Alternating Direction Iteration, RADI), 免除可交换性的苛求, 从而极大地扩充了ADI的应用范围. 同时, 本文还探讨了提高RADI格式效率的若干措施.

关键词: 实正定方阵, 交替方向迭代法, 回归单方向迭代, 计算精度, 并行计算

Abstract:

Alternating direction iteration (ADI) scheme is an effective method for solving real positive definite linear systems; in many cases, however, the method requires that all the direction matrices involved are multiplication exchangeable, which severely limits the scope of application. In this paper, new revised alternating direction iteration (RADI) schemes are proposed, that do not stipulate the multiplication exchangeable requirement, thereby expanding the application scope. In parallel, measures to improve the efficiency of RADI schemes are also discussed.

Key words: real positive definite matrix, alternating direction iteration, regression to a single direction iterative, accuracy of a numerical results, parallel computing

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