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Mathematics of Computation

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Krylov subspace methods for functions of fractional differential operators


Authors: Igor Moret and Paolo Novati
Journal: Math. Comp. 88 (2019), 293-312
MSC (2010): Primary 15A16, 47A56, 65F60, 26A33
DOI: https://doi.org/10.1090/mcom/3332
Published electronically: March 19, 2018
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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.


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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
Email: novati@units.it

DOI: https://doi.org/10.1090/mcom/3332
Keywords: Krylov methods, shift-and-invert Krylov methods, fractional operators, matrix functions
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
Article copyright: © Copyright 2018 American Mathematical Society

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