## Krylov subspace methods for functions of fractional differential operators

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Igor Moret and Paolo Novati
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## Abstract:

The paper deals with the computation of functions of fractional powers of differential operators. The spectral properties of these operators naturally suggest the use of rational approximations. In this view we analyze the convergence properties of the shift-and-invert Krylov method applied to operator functions arising from the numerical solution of differential equations involving fractional diffusion.## References

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## Additional Information

**Igor Moret**- Affiliation: Departments of Mathematics and Geosciences, University of Trieste, 34127 Trieste, Italy
- Email: moret@units.it
**Paolo Novati**- Affiliation: Departments of Mathematics and Geosciences, University of Trieste, 34127 Trieste, Italy
- MR Author ID: 679699
- Email: novati@units.it
- Received by editor(s): November 11, 2016
- Received by editor(s) in revised form: July 2, 2017, and October 8, 2017
- Published electronically: March 19, 2018
- Additional Notes: This work was supported by GNCS-INdAM and by FRA-University of Trieste
- © Copyright 2018 American Mathematical Society
- Journal: Math. Comp.
**88**(2019), 293-312 - MSC (2010): Primary 15A16, 47A56, 65F60, 26A33
- DOI: https://doi.org/10.1090/mcom/3332
- MathSciNet review: 3854059