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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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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.
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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