THE EIGENVALUE PROBLEM EQUIVALENT TO MULTIVARIATE POLYNOMIAL SYSTEM

In this paper, the authors proved that finding all solutions of a given multivariate polynomial system is equivalent to solving a relative joint eigenvalue problem(Theorem 1) and in some cases one can find all solutions of the given system from the eigenvalues and vectors of one matrix or matrix pencil (Theorem 2). Especially the situation that the ideal generated by the given system is 0-dimensional is discussed.     

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

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[x_1,x_2,…,x_n],f(x) can be written as     

Second Equivalence Theorem of Multivariate Polynomial System and Eigenproblem

In[1,2] we have constructed the Joint eigenproblem equivalent to multivariatepolynomial system and presented an algorithm to solve latter.In this paper we willstudy another equivalence theorem for the same problem.The computation of thecorresponding eigenvalues is numerically stable. Consider multivarite polynomial system     

我尊敬的老师徐献瑜教授

徐献瑜教授从三十年代起执教于燕京大学,并主持数学系工作。1952年全国高等院校院系调整后徐先生到北京大学数学力学系任教,于1955年在系内最早地开设“数学实习”课程,并筹建计算数学教研室,主持教研室工作多年。1956年参加全国科学发展规划的制订,为了开创     

评《现代数学新进展》

吴文俊教授主编的“现代数学新进展”由安徽科学技术出版社出版了,许多人对此感到欣慰。这本书中收集了1985年10月由中国科学院系统科学研究所发起并组织的刘徽数学讨论班上我国一些数学专家所作的专题报告。一次为期一周的讨论班当然不可能概括现代数学进展的全貌,但该书在230页的篇幅中涉及到的领域已是够广泛的了。有数理统计,线性规划,     

最小二乘线性逼近的一个注

给定m维实空间中N个点P_i=(x_1~((i)),x_2~((i)),…,x_m~((i)),i=1(1)N.对于任何超平面 k_1x_1+k_2x_2+…+k_mx_m+k_0=0,P_i到它的垂直距离平方和