二元多项式乘积的欧几里得范数的最优化问题  

Optimization Problems of the Euclidean Norm of the Product of Two Polynomials in Two Variables

作　　者：郑观元 张圣贵[1] 

机构地区：[1]福建师范大学数学与计算机科学学院,福建福州350007

出　　处：《武夷学院学报》2013年第5期33-39,共7页Journal of Wuyi University

基　　金：国家自然科学基金项目(11071041)

摘　　要：本文利用分块矩阵方法,定义了二元多项式的欧几里得范数、分块卷积矩阵和分块自相关矩阵等概念,讨论了它们的一些性质,并在给定最高次数的非零二元多项式集合上,建立了两个非零二元多项式乘积的范数与这两个多项式范数的乘积之比的最优化问题与分块自相关Toeplitz矩阵的特征值最优化问题之间的关系.推广了F.Bünger[1]的相应结论.The Euclidean norm, convolution matrix and autocorrelafion matrix of a polynomial in two variables are defined by the method of block matrices, and some of their properties are proved, and the relation between the optimization problem of the norm of the product of two nonzero polynomials over the product of their norms in the set of all nonzero polynomials with the highest degree in two variables and the eigenvalue optimization problem of autocorrelation Toeplitz matrices is constructed.

关 键 词：欧几里得范数 多项式 卷积矩阵 特征值优化问题 

分 类 号：Q174.14[生物学—水生生物学] Q224[生物学—普通生物学]