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Multiple grid methods for the solution of Fredholm integral equations of the second kind


Authors: P. W. Hemker and H. Schippers
Journal: Math. Comp. 36 (1981), 215-232
MSC: Primary 65R20; Secondary 45L10
DOI: https://doi.org/10.1090/S0025-5718-1981-0595054-2
MathSciNet review: 595054
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Abstract: In this paper multiple grid methods are applied for the fast solution of the large nonsparse systems of equations that arise from the discretization of Fredholm integral equations of the second kind. Various multiple grid schemes, both with Nyström and with direct interpolation, are considered. For these iterative methods, the rates of convergence are derived using the collectively compact operator theory by Anselone and Atkinson. Estimates for the asymptotic computational complexity are given, which show that the multiple grid schemes result in $ \mathcal{O}({N^2})$ arithmetic operations.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1981-0595054-2
Keywords: Fredholm integral equations of the second kind, multiple grid methods
Article copyright: © Copyright 1981 American Mathematical Society