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Accurate Computations of Matrix Eigenvalues with Applications to Differential Operators

 

报告题目: Accurate Computations of Matrix Eigenvalues with Applications to Differential Operators

 

报告人:Qiang Ye, University of Kentucky, Lexington, Kentucky, USA

 

时间201267(星期四)1530-1700

 

地点:理科楼数学系A304

 

摘要:For matrix eigenvalue problems arising in discretizations of differential operators, it is usually smaller eigenvalues that well approximate the eigenvalues of the differential operators and are of interest. The finite difference discretization leads to a standard eigenvalue problem $Ax = \lambda x$ and the finite element method results in a generalized eigenvalue problem $Ax = \lambda Bx$, where A (and B) are often diagonally dominant. With the condition number for the discretized problem $A$ (or $B^{-1}A$) typically large, smaller eigenvalues computed are expected to have low relative accuracy.

     In this talk, we present our recent works on high relative accuracy algorithms for computing eigenvalues of diagonally dominant matrices. We present an algorithm that computes all eigenvalues of a symmetric diagonally dominant matrix to high relative accuracy. We further consider using the algorithm in an iterative method for a large scale eigenvalue problem and we show how smaller eigenvalues of finite difference discretizations of differential operators can be computed accurately.Numerical examples are presented to demonstrate the high accuracy achieved by the new algorithm.

 

报告人简介:叶强教授简介:1983年毕业于中国科技大学,获学士学位,1986年在中科院获硕士学位,1989年在加拿大Calgary大学获博士学位。1992-2000年加拿大Manitoba大学数学系助理教授和副教授,2000年至今Kentucky大学数学系教授,2010—2013Ralph E. and Norma L. Edwards研究教授。叶强教授从事数值分析和科学计算的研究,主要领域是数值线性代数和大规模矩阵计算,在大规模矩阵特征值问题、线性方程组等的数值方法理论分析和算法开发上取得了一系列有影响的重要研究成果。

 

联系人:贾仲孝

 

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