A new iterative refinement for ill-conditioned linear systems based on discrete gradient

被引：1
|
作者：
Liu, Kai [1 ]
Yang, Jie [1 ]
Liu, Changying [2 ]
机构：
[1] Nanjing Univ Finance & Econ, Coll Appl Math, Nanjing 210023, Peoples R China
[2] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing 210044, Peoples R China
来源：
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2020年 / 37卷 / 03期
关键词：
Wilkinson's iterative refinement; Ill-conditioned system of linear equations; Discrete gradient method; Gradient system; INTEGRATION;
D O I：
10.1007/s13160-020-00417-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a new iterative refinement for ill-conditioned linear systems is derived based on discrete gradient methods for gradient systems. It is proved that the new method is convergent for any initial values irrespective of the choice of the stepsize h. Some properties of the new iterative refinement are presented. It is shown that the condition number of the coefficient matrix in the linear system to be solved in every step can be improved significantly compared with Wilkinson's iterative refinement. The numerical experiments illustrate that the new method is more effective and efficient than Wilkinson's iterative refinement when dealing with ill-conditioned linear systems.
引用
收藏
页码：803 / 818
页数：16
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