## 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.

Original language | English |
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Pages (from-to) | 604-623 |

Number of pages | 20 |

Journal | Applied Mathematics and Computation |

Volume | 273 |

Early online date | 12 Nov 2015 |

DOIs | |

Publication status | Published - 15 Jan 2016 |

## Keywords

- Fractional calculus
- Iterative solvers
- Low-rank methods
- Preconditioning
- Schur complement
- Sylvester equations
- Tensor equations

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics