NUMERICAL STUDY OF THREE-PARAMETER MATRIX EIGENVALUE PROBLEM BY GRADIENT METHOD
Niranjan Bora, Arun Kumar Baruah · International Journal of Pure and Apllied Mathematics · 2017
In this paper, a Convergent Gradient Method, which was first developed to solve generalised eigenvalue problem of the form Ax = λBx, 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.