Fast tensor product solvers for optimization problems with fractional differential equations as constraints / Sergey Dolgov, John W. Pearson, Dmitry V. Savostyanov, Martin Stoll
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870664042
URN
urn:nbn:de:gbv:3:2-64662
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Beiträger
Erschienen
Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, January 9, 2015
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1 Online-Ressource (32 Seiten = 2,19 MB) : Diagramme
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Sprache
eng
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Inhaltliche Zusammenfassung
Abstract: Fractional differential equations have recently received much attention within computational mathematics and applied science, and their numerical treatment is an important research area as such equations pose substantial challenges to existing algorithms. An optimization problem with constraints given by fractional differential equations is considered, which in its discretized form leads to a high-dimensional tensor equation. The solution to such equations is presented in the tensor-train format. We compare three types of solution strategies that employ sophisticated iterative techniques using either preconditioned Krylov solvers or tailored alternating schemes. The competitiveness of these approaches is presented using several examples.
Schriftenreihe
Max Planck Institute Magdeburg Preprints ; 14-25 ppn:870173030