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Fast tensor product solvers for optimization problems with fractional differential equations as constraints

Dolgov, Sergey and Pearson, John W and Savostyanov, Dmitry V and Stoll, Martin (2016) 'Fast tensor product solvers for optimization problems with fractional differential equations as constraints.' Applied Mathematics and Computation, 273. pp. 604-623. ISSN 0096-3003

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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. To reduce the computation time and storage, the solution is sought 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 with constant and variable coefficients.

Item Type: Article
Uncontrolled Keywords: Fractional calculus; Iterative solvers; Sylvester equations; Preconditioning; Low-rank methods; Tensor equations; Schur complement
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 05 Nov 2020 18:27
Last Modified: 18 Aug 2022 11:23
URI: http://repository.essex.ac.uk/id/eprint/26647

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