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Linear Complexity Solution of Parabolic Integro-differential Equations |
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| Authors: | A. -M. Matache C. Schwab T. P. Wihler |
| Affiliation: | (1) Bank Julius Baer & Co. Ltd. Private Banking, Bahnhofstrasse 36, 8010 Zürich, Switzerland;(2) Seminar for Applied Mathematics, ETH Zürich, 8092 Zürich, Switzerland;(3) Department of Mathematics and Statistics, McGill University, Montreal, QC, H3A 2K6, Canada |
| Abstract: | The numerical solution of parabolic problems with a pseudo-differential operator by wavelet discretization in space and hp discontinuous Galerkin time stepping is analyzed. It is proved that an approximation for u(T) can be obtained in N points with accuracy for any integer p ≥ 1 in work and memory which grows logarithmically-linear in N.Supported in part IHP Network Breaking Complexity of the EC (contract number HPRN-CT-2002-00286) with support by the Swiss Federal Office for Science and Education under grant No. BBW 02.0418.Funded by the Swiss National Science Foundation (Grant PBEZ2-102321). |
| Keywords: | Parabolic equations Integro-differential operators Discontinuous Galerkin methods Wavelets Matrix compression GMRES Computational finance Option pricing |
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