In this paper we propose a new choice of poles to define reliable rational Krylov methods. These methods are used for approximating function of positive definite matrices. In particular, the fractional power and the fractional resolvent are considered because of their importance in the numerical solution of fractional partial differential equations. The numerical experiments on some fractional partial differential equation models confirm that the proposed approach is promising.
Rational Krylov methods for functions of matrices with applications to fractional partial differential equations
Lidia Aceto;Fabio Durastante;
2019-01-01
Abstract
In this paper we propose a new choice of poles to define reliable rational Krylov methods. These methods are used for approximating function of positive definite matrices. In particular, the fractional power and the fractional resolvent are considered because of their importance in the numerical solution of fractional partial differential equations. The numerical experiments on some fractional partial differential equation models confirm that the proposed approach is promising.File in questo prodotto:
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KrylovJacobi-revised.pdf
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