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A degenerate kernel method for eigenvalue problems of compact integral operators

Gnaneshwar, N (2007) A degenerate kernel method for eigenvalue problems of compact integral operators. In: Advances in Computational Mathematics, 27 (3). pp. 339-354.

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Abstract

We consider the approximation of eigenfunctions of a compact integral operator with a smooth kernel by a degenerate kernel method. By interpolating the kernel of the integral operator in both the variables, we prove that the error bounds for eigenvalues and for the distance between the spectral subspaces are of the orders $h^{2r}$ and $h^r$ respectively. By iterating the eigenfunctions we show that the error bounds for eigenfunctions are of the orders $h^{2r}$.We give the numerical results.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Springer Netherlands
Keywords: convergence rates, degenerate kernel, eigenvalue problem, integral operator
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 23 Feb 2008
Last Modified: 19 Sep 2010 04:42
URI: http://eprints.iisc.ernet.in/id/eprint/12865

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