多元齐次多项式定号性判别方法

DEFINITENESS OF MULTI VARIABLE HOMOGENEOUS POLYNOMIAL

研究了多元齐次多项式的定号性．利用齐次多项式的特殊性以及计算机的高速运算能力，构造了一个数值判别算法，并证明了这一算法在概率意义上的正确性．这一算法已经被编程实现应用于三元，四元齐次多项式定号性的判别中．这一算法还可以在构造李亚普诺夫函数时获得应用．

This paper studies definiteness of multi variable homogeneous polynomials.Based on the special character of homogeneous polynomials and ability of modern computers,a digital algorithm was designed to judge the definiteness of homogeneous polynomials.It was also proved that this numeric method is correct in the sense of probability.The algorithm was programmed for judging stability of homogeneous polynomials of three and four variables,and it has a lot of value for finding Lyapunov functions in stability judgment of nonlinear systems.