多项式组的Hankel型广义子结式  

Hankel Generalized Subresultants for Several Univariate Polynomials

作　　者：蒙嘉奇 王伟东 杨静[1,2] MENG Jiaqi;WANG Weidong;YANG Jing(School of Mathematics and Physics,Center for Applied Mathematics of Guangxi,Guangxi Minzu University,Nanning 530006,China;Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis,Nanning 530006,China)

机构地区：[1]广西民族大学数学与物理学院,广西应用数学中心,广西南宁530006 [2]广西混杂计算与集成电路设计分析重点实验室,广西南宁530006

出　　处：《应用数学》2024年第4期982-995,共14页Mathematica Applicata

基　　金：国家自然科学基金数学天元基金项目(12326353);广西自然科学基金(桂科2023GXNSF-BA026019);广西民族大学自然科学类培育项目(2022MDKJ001)。

摘　　要：本文构造了一种新的多项式组广义子结式矩阵,即Hankel型广义子结式矩阵,并证明该矩阵在Horner基下的行列式多项式即为多项式组的广义子结式,由此给出了多项式组广义子结式在Horner基下的表示形式,从而将两个多项式的Hankel型子结式推广到多项式组的情形.实验结果表明,Hankel型广义子结式在计算中低阶多项式组广义子结式时的性能优于其他已知类型的广义子结式.In this paper,a new type of generalized subresultant matrix,i.e.,the Hankel-type generalized subresultant matrix,is constructed for a polynomial set.It is proved that the determinant polynomial of the resulting matrix in Horner basis is the generalized subresultant polynomial of the given polynomial set,which provides an expression for the generalized subresultant polynomial in Horner basis.This extends the formulation of Hankel-type subresultant polynomials from two polynomials to a polynomial set.Experimental results show that the Hankel-type formula for the generalized subresultant polynomial performs better than other known formulas when applied to compute generalized subresultant polynomials with low/medium orders.

关 键 词：结式矩阵 HANKEL矩阵 Horner基 广义子结式 

分 类 号：O174.14[理学—数学]