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Use of extrapolation for improving the order of convergence of eigenelement approximations

DSpace at IIT Bombay

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Field Value
 
Title Use of extrapolation for improving the order of convergence of eigenelement approximations
 
Creator KULKARNI, RP
 
Subject integral-equations
eigenvalues
 
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.
 
Publisher OXFORD UNIV PRESS
 
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
 
Type Article
 
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
 
Language en