Summary
2011 International Symposium on Nonlinear Theory and Its Applications
2011
Session Number:A2L-A
Session:
Number:A2L-A1
Computing Tight Bounds on Extreme Eigenvalues of Symmetric Matrices
Takeshi Ogita,
pp.84-84
Publication Date:2011/9/4
Online ISSN:2188-5079
Summary:
This paper is concerned with verifying the accuracy of computed matrix eigenvalues, especially minimum or maximum eigenvalue of a symmetric matrix. It is useful to compute sharp bounds on such extreme eigen- values because it becomes essentially important (and frequently ineludible) in verified numerical computations, e.g. for solutions of linear and nonlinear systems. In this paper, an algorithm for computing tight bounds for the extreme eigenvalues is developed for symmetric matrices. Numerical results are presented showing the performance of the proposed algorithm.