华东师范大学学报（自然科学版） >

2022 , Vol. 2022 >Issue 4: 1 - 12

DOI: https://doi.org/10.3969/j.issn.1000-5641.2022.04.001

数学

解实正定线性方程组的交替方向迭代法新格式

  • 征道生
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  • 华东师范大学 数学科学学院, 上海　200241
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

收稿日期: 2021-01-27

  网络出版日期: 2022-07-19

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

  • Daosheng ZHENG
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  • School of Mathematical Sciences, East China Normal University, Shanghai　200241, China

Received date: 2021-01-27

  Online 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

本文引用格式

征道生 . 解实正定线性方程组的交替方向迭代法新格式[J]. 华东师范大学学报（自然科学版）, 2022 , 2022(4) : 1 -12 . DOI: 10.3969/j.issn.1000-5641.2022.04.001

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

参考文献

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