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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