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

Author

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  • Dolgov, Sergey
  • Pearson, John W.
  • Savostyanov, Dmitry V.
  • Stoll, Martin

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.

Suggested Citation

  • Dolgov, Sergey & Pearson, John W. & Savostyanov, Dmitry V. & Stoll, Martin, 2016. "Fast tensor product solvers for optimization problems with fractional differential equations as constraints," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 604-623.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:604-623
    DOI: 10.1016/j.amc.2015.09.042
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    Cited by:

    1. Xiao, Lin & Li, Xiaopeng & Jia, Lei & Liu, Sai, 2022. "Improved finite-time solutions to time-varying Sylvester tensor equation via zeroing neural networks," Applied Mathematics and Computation, Elsevier, vol. 416(C).

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