线性约束下实二次型有定或不定性的一个判别算法

AN ALGORITHM FOR DISCRIMINATING DEFINITE OR NON DEFINITE REAL QUADRATIC FORMS WITH LINEAR RESTRICTION

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.