Title: Eigenvalues bounds for symmetric interval matrices

Authors: Sukhjit Singh; D.K. Gupta

Addresses: Department of Mathematics, Indian Institute of Technology, Kharagpur 721 302, West Bengal, India ' Department of Mathematics, Indian Institute of Technology, Kharagpur 721 302, West Bengal, India

Abstract: The aim of this paper is to approximate the eigenvalues bounds of real symmetric interval matrices as sharp as possible. Using the concepts of interval analysis, this is done by solving the standard interval eigenvalue problem by applying the interval extension of the single step eigen perturbation method. The deviation amplitude of the interval matrix is considered as a perturbation around the nominal value of the interval matrix. The mathematical formulation of the method is described. Two numerical examples are worked out and the results obtained are compared with the results of existing methods. It is observed that our method is reliable, efficient and gives better results for all examples considered.

Keywords: interval analysis; perturbation theory; symmetric interval matrix; computational speed; reliability; stochastic analysis; eigenvalues bounds; deviation amplitude.

DOI: 10.1504/IJCSM.2015.071808

International Journal of Computing Science and Mathematics, 2015 Vol.6 No.4, pp.311 - 322

Received: 07 May 2013
Accepted: 19 Jan 2014
Published online: 19 Sep 2015 *

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