Eigenvalues for infinite matrices |
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Institution: | Department of Applied Mathematics University of Manitoba Winnipeg, Manitoba, Canada R3T 2N2;Department of Mathematics Bangalore University Bangalore 560 001, India |
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Abstract: | 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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