Skip to main content

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

Dolgov, Sergey, Pearson, John W, Savostyanov, Dmitry V, Stoll, Martin (2015) Fast tensor product solvers for optimization problems with fractional differential equations as constraints. Applied Mathematics and Computation, 273 . pp. 604-623. ISSN 0096-3003. (doi:10.1016/j.amc.2015.09.042) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
https://doi.org/10.1016/j.amc.2015.09.042

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.

Item Type: Article
DOI/Identification number: 10.1016/j.amc.2015.09.042
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: John Pearson
Date Deposited: 30 Apr 2015 17:14 UTC
Last Modified: 29 May 2019 14:28 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/48162 (The current URI for this page, for reference purposes)
  • Depositors only (login required):