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Richardson extrapolation of iterated discrete projection methods for eigenvalue approximation

✍ Scribed by Zhongying Chen; Guangqing Long; Gnaneshwar Nelakanti

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 635 KB
Volume: 223
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.12.019

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✦ Synopsis

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.

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## Abstract Several Krylov subspace iterative algorithms are compared as the solvers for the discrete dipole approximation method to analyze the electromagnetic scattering problem. Fast Fourier transform technique is exploited to accelerate the computation of matrix‐vector product. Numerical exampl