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学术报告一百零八:Accurate eigenvalues of some generalized sign regular matrices via relatively robust representations

时间:2021-01-07 10:48

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数学与统计学院学术报告[2020] 108

(高水平大学建设系列报告461)

报告题目: Accurate eigenvalues of some generalized sign regular matrices  via relatively robust representations

报告人: 黄荣  教授 (湖南科技大学

报告时间:202011229: 30-10: 30

报告地点: 汇星楼514

报告内容:In this talk, we consider how to accurately solve the nonsymmetric eigenvalue problem for a class of  generalized sign regular matrices including extremely ill-conditioned quasi-Cauchy and quasi-Vandermonde matrices. The problem of performing accurate computations with structured matrices is very much a representation problem. We first develop a relatively robust representation (RRR) for this class of matrices by introducing a free parameter, which exceeds an essential threshold, into an indefinite factorization. We then design a new O(n^3) algorithm to compute  all the eigenvalues  of such  matrices with high relative accuracy,  as warranted by the RRR. Error analysis and numerical experiments are performed to illustrate the  high relative accuracy.

报告人简历:黄荣,教授、博士生导师,湖南省杰出青年基金获得者、入选湖南省芙蓉学者、湖南省普通高校学科带头人、湖南省新世纪121人才工程人选、湖南省普通高校青年骨干教师,现任湖南科技大学数学与计算科学学院院长。主要从事数值计算方面的研究工作,已主持国家自然科学基金面上项目、国家自然科学基金青年项目、湖南省杰出青年基金、教育部博士点基金、中国博士后基金等,研究成果全部以第一作者方式发表在Math. Comput.SIAM. J. Matrix Anal. Appl.J. Sci. ComputBITJ. Comput. Appl. Math.Numer. Linear Algebra Appl.Numer. Algor.Linear Algebra Appl.等国际学术期刊上。


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