Eigenvalues for infinite matrices

Shivakumar, P. N. ; Williams, J. J. ; Rudraiah, N. (1987) Eigenvalues for infinite matrices Linear Algebra and its Applications, 96 . pp. 35-63. ISSN 0024-3795

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/002437...

Related URL: http://dx.doi.org/10.1016/0024-3795(87)90335-1


This paper is concerned with the problem of determining the location of eigenvalues for diagonally dominant infinite matrices; upper and lower bounds for eigenvalues are established. For tridiagonal matrices, a numerical procedure for improving the bounds is given, and the approximation of the eigenvectors is also discussed. The techniques are illustrated for the solution of the well-known Mathieu's equation.

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