**Preprint series:** 05-03, Reports on Numerical Mathematics

B. I. Bandyrskii

**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 numbe of an eigenvalue. The asymptotical behavior of the distance between neighboring eigenvalues is investigated in the case when the order number tends to infinity. Numerical examples are given.

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

**Upload:** 2005-03-30

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