Resultant Elimination via Implicit Equation Interpolation

作     者：TANG Min YANG Zhengfeng ZENG Zhenbing 

作者机构：Shanghai Key Laboratory of Trustworthy Computing East China Normal University Department of Mathematics Shanghai University 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2016年第29卷第5期

页      面：1411-1435页

核心收录：

学科分类：0810[工学-信息与通信工程] 1205[管理学-图书情报与档案管理] 07[理学] 0811[工学-控制科学与工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：supported in part by the National Natural Science Foundation of China under Grant Nos.11471209,61321064 and 61361136002 the Innovation Program of Shanghai Municipal Education Commission under Grant No.14ZZ046 

主　　题：Elimination implicit equations interpolation resultants. 

摘      要：It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the authors combine multivariate implicit equation interpolation and multivariate resultant elimination to compute the reduced resultants, in which the technique of multivariate implicit equation interpolation is achieved by some high probability algorithms on multivariate polynomial interpolation and univariate rational function interpolation. As an application of resultant elimination, the authors illustrate the proposed algorithm on three well-known unsolved combinatorial geometric optimization problems. The experiments show that the proposed approach of resultant elimination is more efficient than some existing resultant elimination methods on these difficult problems.