RESEARCH ANNOUNCEMENTS——The Construction of Eigenvalue Problem Equivalent to Multivariate Polynomial System and the Groebner Basis

作     者：冯果忱,吴文达,黄铠 

作者机构：Jilin University Changchun 130023 Jilin P.R.C. Jilin University Changchun 130023 Jilin P.R.C. Beijing Municipal Computer Center Beijing 100005 P.R.C 

出 版 物：《数学进展》 (Advances in Mathematics(CHINA))

年 卷 期：1993年第3期

页      面：282-284页

核心收录：

基　　金：State Major Key Project for Basic Researches in China 

主　　题：LP The Construction of Eigenvalue Problem Equivalent to Multivariate Polynomial System and the Groebner Basis RESEARCH ANNOUNCEMENTS 

摘      要：In this paper we will show that one cau build up a joint eigenvalue problem eq-uivalent to the. given system. By this way, finding the solutions of the given systemis equivalent to finding all eigenvalues and eigenvectors of one matrix or matrix pen-cil. For the special case that the system has finite isolated solutions, we can obtainall solutions through computing the eigenvalues and eigenvectors of a matrix whichcan Le obtained by Gauss-Jordan elimination. Furthermore, we also find that one canget Groebner Basis for the ideal geuerated by the given system iu this way. For any polynomial f（x）∈K[x1,x2,…,x_n],f（x） can be written as