摘要
针对经济学中较为常见的判别线性约束下实二次型的正定性问题,研究了实对称矩阵的有关性质,提出了一个判别一般实对称矩阵是(半)正定、(半)负定或不定矩阵的有效而实用的算法,较好地解决了带线性约束与无约束的实二次型有定或不定性的判别问题.所述算法具有计算量小,数值计算稳定,易于编程实现等优点.最后给出了计算实例.
This paper discusses the properties on a real symmetric matrix, and presents an algorithm for discriminating a real symmetric matrix into a positive (semi ) definite, negative (semi )definite or non definite matrix. This algorithm is effective and practicable for discriminating definite or non definite real quadratic forms with linear restriction. The algorithm has some obvious advantages such as small operation numbers, computer programming being easy and the stability of numerical computation. The practical computing examples are given.
出处
《华中师范大学学报(自然科学版)》
CAS
CSCD
北大核心
1997年第4期405-409,共5页
Journal of Central China Normal University:Natural Sciences
基金
国家"九五"重点科技攻关
关键词
实二次型
正定性
矩阵分解
经济学
线性约束
real quadratic form
positive definiteness
matrix decomposition
Householder transformation