Richardson extrapolation of iterated discrete projection methods for eigenvalue approximation

Authors:
Zhongying Chen;Guangqing Long;Gnaneshwar Nelakanti
Affiliations:
Department of Scientific Computing and Computer Applications, Sun Yat-sen University, Guangzhou 510275, PR China;Department of Mathematics, Guangxi Normal College, Nanning 530001, PR China and Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, 100080, PR China;Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, West Bengal, India
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, the eigenvalue approximation of a compact integral operator with a smooth kernel is discussed. We propose asymptotic error expansions of the iterated discrete Galerkin and iterated discrete collocation methods, and asymptotic error expansion of approximate eigenvalues. We then apply Richardson extrapolation to obtain higher order super-convergence of eigenvalue approximations. Numerical examples are presented to illustrate the theoretical estimate.