IJPAM: Volume 112, No. 1 (2017)

Title

NUMERICAL STUDY OF THREE-PARAMETER MATRIX
EIGENVALUE PROBLEM BY GRADIENT METHOD

Authors

Niranjan Bora$^1$, Arun Kumar Baruah$^2$
$^{1,2}$Department of Mathematics, DUIET
Dibrugarh University
Dibrugarh, 786004, Assam, INDIA

Abstract

In this paper, a Convergent Gradient Method, which was first developed to solve generalised eigenvalue problem of the form $Ax=\lambda Bx$, will be used to find approximate eigenvalues and corresponding eigenvectors of Multiparameter Matrix Eigenvalue Problems (MMEPs). To apply Gradient Method, we will reduce MMEPs into a single matrix pencil containing the block diagonal matrices. Although the Method can be extended to Multiparameter case, but the whole work is done by considering three-parameter case only to relax computational cost. Computational efficiency of this method will be discussed by comparing the results with Kronecker Product Method as proposed by Atkinson in $1960$, analytically with the help of numerical examples.

History

Received: February 25, 2016
Revised: October 24, 2016
Published: January 26, 2017

AMS Classification, Key Words

AMS Subject Classification: 35PXX, 65FXX, 65F15, 35A35
Key Words and Phrases: multiparameter matrix eigenvalue problems, Kroneecker product, tensor product space, convergent gradient method

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How to Cite?

DOI: 10.12732/ijpam.v112i1.10 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 112
Issue: 1
Pages: 125 - 135


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