基于条件数与行范数的有限逼近算法

 隋树林a, 陈海燕a, 邵巍b

（青岛科技大学 a.数理学院；b.自动化与电子工程学院，山东 青岛 266061）

 摘要： 针对一类系数矩阵行数远大于列数的大型线性方程组,根据有限截断理论以及矩阵的相关性质,提出一种基于条件数和行范数的有限逼近算法。利用该算法截断原方程,以截断方程的解代替原解。实验数据表明,该算法不仅简化了计算的复杂度,而且提高了解决实际问题的可行性。

 关键词： 有限截断算法; 线性方程组; 条件数; 范数

中图分类号： O 241             文献标志码：  A

 Finite Approximation Algorithm Based on Condition Number and Row Norm

 SUI Shulina, CHEN Haiyana, SHAO Weib

 (a. College of Mathematics and Physics； b. College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao 266061，China)

Abstract： This paper for a class of coefficient matrix rows is greater than the number of columns of the largescale system of linear equations, puts forward a finite approximation algorithm based on row norm and condition number according to the theory of the finite section method and the related properties of the matrix.This algorithm is used to truncate the original equations, thus the solution of the original equations can be replaced with the solution of the truncated equations.Experimental data show that this algorithm not only simplifies the computing complexity， but also improve the feasibility of resolving practical problems.

 Key words：  finite section method; linear equations; condition number; norm

  收稿日期： 20141105

 基金项目： 国家自然科学基金项目（61104187）；山东省优秀中青年科学家科研奖励基金项目（BS2012NY003）；青岛市科技计划基础研究项目（1314227jch）.

作者简介： 隋树林（1958—），男，教授.