Rational Krylov methods for functions of matrices with applications to fractional partial differential equations

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 results of the numerical experiments we have carried out on some fractional models confirm that the proposed approach is promising.

References in corpus (1)

• Rational approximations to fractional powers of self-adjoint positive operators

Cited by in corpus (5)

• Fast and accurate approximations to fractional powers of operators
• Exponentially convergent trapezoidal rules to approximate fractional powers of operators
• Nonlocal diffusion of variable order on complex networks
• An a posteriori error estimator for the spectral fractional power of the Laplacian
• Padé-type approximations to the resolvent of fractional powers of operators