A new superconvergent collocation method for eigenvalue problems

Author:
Rekha P. Kulkarni

Journal:
Math. Comp. **75** (2006), 847-857

MSC (2000):
Primary 47A10, 47A58, 47A75, 65J99, 65R20

DOI:
https://doi.org/10.1090/S0025-5718-06-01871-0

Published electronically:
January 3, 2006

MathSciNet review:
2196995

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Abstract: Here we propose a new method based on projections for the approximate solution of eigenvalue problems. For an integral operator with a smooth kernel, using an interpolatory projection at Gauss points onto the space of (discontinuous) piecewise polynomials of degree , we show that the proposed method exhibits an error of the order of for eigenvalue approximation and of the order of for spectral subspace approximation. In the case of a simple eigenvalue, we show that by using an iteration technique, an eigenvector approximation of the order can be obtained. This improves upon the order for eigenvalue approximation in the collocation/iterated collocation method and the orders and for spectral subspace approximation in the collocation method and the iterated collocation method, respectively. We illustrate this improvement in the order of convergence by numerical examples.

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Additional Information

**Rekha P. Kulkarni**

Affiliation:
Department of Mathematics, Indian Institute of Technology, Powai, Mumbai 400 076, India

Email:
rpk@math.iitb.ac.in

DOI:
https://doi.org/10.1090/S0025-5718-06-01871-0

Keywords:
Eigenvalue,
spectral subspace,
integral equations,
collocation,
Gauss points

Received by editor(s):
March 2, 2003

Received by editor(s) in revised form:
October 28, 2004

Published electronically:
January 3, 2006

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.