Use of extrapolation for improving the order of convergence of eigenelement approximations
DSpace at IIT Bombay
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Title |
Use of extrapolation for improving the order of convergence of eigenelement approximations
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Creator |
KULKARNI, RP
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Subject |
integral-equations
eigenvalues |
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Description |
We consider the approximation of the eigenelements of a compact integral operator defined on C[0, 1] with a smooth kernel. We use the iterated collocation method based on r Gauss points and piecewise polynomials of degree less than or equal to r - 1 on each subinterval of a nonuniform partition of [0,1]. We obtain asymptotic expansions for the arithmetic means of m eigenvalues and also for the associated spectral projections. Using Richardson extrapolation, we show that the order of convergence O(h(2r)) in the iterated collocation method can be improved to O(h(2r+2)). Similar results hold for the Nystrom method and for the iterated Galerkin method. We illustrate the improvement in the order of convergence by numerical experiments.
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Publisher |
OXFORD UNIV PRESS
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Date |
2011-08-22T07:35:18Z
2011-12-26T12:56:15Z 2011-12-27T05:44:41Z 2011-08-22T07:35:18Z 2011-12-26T12:56:15Z 2011-12-27T05:44:41Z 1997 |
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Type |
Article
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Identifier |
IMA JOURNAL OF NUMERICAL ANALYSIS, 17(2), 271-284
0272-4979 http://dx.doi.org/10.1093/imanum/17.2.271 http://dspace.library.iitb.ac.in/xmlui/handle/10054/10360 http://hdl.handle.net/10054/10360 |
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Language |
en
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