迷人的最大特征对子（英文）  

The Charming Leading Eigenpair

作　　者：陈木法[1] 

机构地区：[1]北京师范大学数学科学学院,北京100875

出　　处：《数学进展》2017年第4期481-497,共17页Advances in Mathematics（China）

基　　金：supported in part by NSFC(No.11131003,No.11626245);the "985" Project from the Ministry of Education in China;the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions

摘　　要："主导特征对子"在不同场合有不同名称.在矩阵论中称为最大特征对子(最大特征值及其对应的特征向量).本文首先介绍计算矩阵最大特征对子的十分意外的新结果.主要贡献是选取一个熟知算法的高效初值.其想法来源于我们新近关于主导特征值估计的研究.第二部分里,我们介绍很幸运得到的关于主导特征值的统一估计.第三部分通过一个特别例子说明此项研究的源头.最后概述我们关于主导特征值估计和更一般的各种稳定性速度研究的漫长历程.The leading eigenpair （the couple of eigenvalue and its eigenvector） or the first nontrivial one has different names in different contexts. It is the maximal one in the matrix theory. The talk starts from our new results on computing the maximal eigenpair of matrices. For the unexpected results, our contribution is the efficient initial value for a known algorithm. The initial value comes from our recent theoretic study on the estimation of the leading eigenvalues. To which we have luckily obtained unified estimates which consist of the second part of the talk. In the third part of the talk, the original motivation of the study along this direction is explained in terms of a specific model. The paper is concluded by a brief overview of our study on the leading eigenvalue, or more generally on the speed of various stabilities.

关 键 词：主导特征对子 高效初值 三对角阵 速度估计 Hardy(Poincare)型不等式 φ4模型 

分 类 号：O151.21[理学—数学] O211.62[理学—基础数学]