Exponentially Convergent Trapezoidal Rules to Approximate Fractional Powers of Operators-Reference-Cited by-同舟云学术

Exponentially Convergent Trapezoidal Rules to Approximate Fractional Powers of Operators

Published:2022-04-04 Issue:2 Volume:91 Page:
ISSN:0885-7474
Container-title:Journal of Scientific Computing
language:en
Short-container-title:J Sci Comput

Author:

Aceto Lidia^ORCID,Novati Paolo

Abstract

AbstractIn this paper we are interested in the approximation of fractional powers of self-adjoint positive operators. Starting from the integral representation of the operators, we apply the trapezoidal rule combined with a double-exponential transform of the integrand function. In this work we show how to improve the existing error estimates for the scalar case and also extend the analysis to operators. We report some numerical experiments to show the reliability of the estimates obtained.

Funder

INdAM-GNCS

FRA-University of Trieste

Publisher

Springer Science and Business Media LLC

Subject

Computational Theory and Mathematics,General Engineering,Theoretical Computer Science,Software,Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://link.springer.com/content/pdf/10.1007/s10915-022-01837-4.pdf

Reference21 articles.

1. Aceto, L., Bertaccini, D., Durastante, F., Novati, P.: Rational Krylov methods for functions of matrices with applications to fractional partial differential equations. J. Comput. Phys. 396, 470–482 (2019)

2. Aceto, L., Novati, P.: Fast and accurate approximations to fractional powers of operators. IMA J. Numer. Anal. (2021). https://doi.org/10.1093/imanum/drab002

3. Aceto, L., Novati, P.: Padé-type approximations to the resolvent of fractional powers of operators. J. Sci. Comput. 83(1), 1–17 (2020)

4. Aceto, L., Novati, P.: Rational approximations to fractional powers of self-adjoint positive operators. Numer. Math. 143, 1–16 (2019)

5. Balakrishnan, A.V.: Fractional powers of closed operators and the semigroups generated by them. Pac. J. Math. 10, 419–437 (1960)

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