HGR多项式根的交错分布定理  

On Staggered Distribution Theorem of HGR Polynomial Roots

作　　者：刘建强 LIU Jian-qiang(School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China)

机构地区：[1]宁夏大学数学统计学院,银川750021

出　　处：《西南师范大学学报（自然科学版）》2020年第9期1-5,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：宁夏高等学校科学技术研究项目(NCY2018047);国家自然科学基金项目(61662060);宁夏自然科学基金项目(2020AAC03030).

摘　　要：乘积匹配是构造多任务核的一种基本方法,HGR多项式则为乘积匹配多项式的存在性提供了判定依据.运用数学归纳法等方法,研究了HGR多项式的性质,包括其首项系数、次数、对应连分式定义域的包含关系、根的交错分布等,在此基础上提出并证明了HGR多项式根的交错分布定理,最后举例说明了该定理的作用.Product-matching is a basic method for constructing multi-task kernels.HGR polynomials offer evidences for the existence of the product-matching polynomials.With mathematical induction,we have studied their properties including leading coefficients,orders,the containment relationship of domains of their corresponding continued fractions and the staggered distributing properties.Then based on these properties,we have proposed and proved the staggered distribution theorem of HGR polynomials.At last,we show the application of the staggered distribution theorem by an example.

关 键 词：交错分布 乘积匹配多项式 根的分布 HGR系统 

分 类 号：O29[理学—应用数学]