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dc.contributor.authorDruskin, Vladimir
dc.contributor.authorLieberman, Chad E.
dc.contributor.authorZaslavsky, Mikhail
dc.date.accessioned2011-01-14T18:40:10Z
dc.date.available2011-01-14T18:40:10Z
dc.date.issued2010-08
dc.date.submitted2009-10
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.urihttp://hdl.handle.net/1721.1/60578
dc.description.abstractWe compute $u(t)=\exp(-tA)\varphi$ using rational Krylov subspace reduction for $0\leq t<\infty$, where $u(t),\varphi\in\mathbf{R}^N$ and $0<A=A^*\in\mathbf{R}^{N\times N}$. A priori optimization of the rational Krylov subspaces for this problem was considered in [V. Druskin, L. Knizhnerman, and M. Zaslavsky, SIAM J. Sci. Comput., 31 (2009), pp. 3760–3780]. There was suggested an algorithm generating sequences of equidistributed shifts, which are asymptotically optimal for the cases with uniform spectral distributions. Here we develop a recursive greedy algorithm for choice of shifts taking into account nonuniformity of the spectrum. The algorithm is based on an explicit formula for the residual in the frequency domain allowing adaptive shift optimization at negligible cost. The effectiveness of the developed approach is demonstrated in an example of the three-dimensional diffusion problem for Maxwell's equation arising in geophysical exploration. We compare our approach with the one using the above-mentioned equidistributed sequences of shifts. Numerical examples show that our algorithm is able to adapt to the spectral density of operator $A$. For examples with near-uniform spectral distributions, both algorithms show the same convergence rates, but the new algorithm produces superior convergence for cases with nonuniform spectra.en_US
dc.language.isoen_US
dc.publisherSociety of Industrial and Applied Mathematics (SIAM)en_US
dc.relation.isversionofhttp://dx.doi.org/10.1137/090774082en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSIAMen_US
dc.titleOn Adaptive Choice of Shifts in Rational Krylov Subspace Reduction of Evolutionary Problemsen_US
dc.typeArticleen_US
dc.identifier.citationDruskin, Vladimir, Chad Lieberman, and Mikhail Zaslavsky. “On Adaptive Choice of Shifts in Rational Krylov Subspace Reduction of Evolutionary Problems.” SIAM Journal on Scientific Computing 32.5 (2010): 2485-2496. Print.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Aeronautics and Astronauticsen_US
dc.contributor.approverLieberman, Chad E.
dc.contributor.mitauthorLieberman, Chad E.
dc.relation.journalSIAM Journal on Scientific Computingen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsDruskin, Vladimir; Lieberman, Chad; Zaslavsky, Mikhailen
mit.licensePUBLISHER_POLICYen_US


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