A new superconvergent collocation method for eigenvalue problems
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- by Rekha P. Kulkarni PDF
- Math. Comp. 75 (2006), 847-857 Request permission
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 $\leq r-1$, we show that the proposed method exhibits an error of the order of $4r$ for eigenvalue approximation and of the order of $3r$ 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 $4r$ can be obtained. This improves upon the order $2r$ for eigenvalue approximation in the collocation/iterated collocation method and the orders $r$ and $2r$ 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.References
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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
- Received by editor(s): March 2, 2003
- Received by editor(s) in revised form: October 28, 2004
- Published electronically: January 3, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2196995