关于多项式惯性的Hermite-Fujiwara定理的改进(英文)  

IMPROVEMENT OF HERMITE-FUJIWARA THEOREM FOR THE INERTIA OF POLYNOMIALS

作　　者：胡永建[1] 詹旭洲[1] 陈公宁[1] 

机构地区：[1]北京师范大学数学科学学院数学与复杂系统教育部重点实验室,北京100875

出　　处：《高等学校计算数学学报》2014年第4期327-344,共18页Numerical Mathematics A Journal of Chinese Universities

基　　金：Supported by grants from the National Natural Science Foundation of China(Nos.11071017and 11271045);the Program for New Century Excellent Talents in University

摘　　要：In this paper,we first present an improvement of the well-known Hermite-Fujiwara theorem for the inertia of polynomials,and then use it to deduce some explicit formulas for the number of roots of a complex polynomial located in a given interval of the real axis in terms of the inertia of Bezout or Hankel matrices.In this paper, we first present an improvement of the well-known Hermite-Fujiwara theorem for the inertia of polynomials, and then use it to deduce some explicit formulas for the number of roots of a complex polynomial located in a given interval of the real axis in terms of the inertia of Bezout or Hankel matrices.

关 键 词：inertia of polynomial inertia of matrix Bezout matrix Hankel matrix Hermite-Fujiwara theorem. 

分 类 号：O241.6[理学—计算数学] O151.2[理学—数学]