An algorithm for matrix Sturm-Liouville problems based on a piece-wise constant perturbation of the differential operator

by    B. I. Bandyrskii, I. P. Gavrilyuk, I. I. Lazurchak, V. L. Makarov

Preprint series: 05-07, Reports on Numerical Mathematics

B. I. Bandyrskii, I. P. Gavrilyuk, I. I. Lazurchak, V. L. Makarov

Preprint series: , Reports on Numerical Mathematics

MSC:
65L15 Eigenvalue problems
65Y20 Complexity and performance of numerical algorithms [See also 68Q25]
34D10 Perturbations
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum
34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions

Abstract: A new algorithm for Sturm-Liouville problems with matrix coefficients is proposed which possesses the convergence rate of a geometric progression with a denominator depending inversely proportional from the order number of eigenvalues. The asymptotical behavior of the distance between neighboring eigenvalues when the order number tends to infinity is investigated too.

Keywords: Sturm-Liouville problem with matrix coefficients, asymptotic expansions, apriori estimates

Upload: 2005-06-27

Update: 2005


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