Rational approximations to fractional powers of self-adjoint positive operators

Abstract

We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in approximation theory involving Padé approximants. The analysis improves some existing results and the numerical experiments proves its accuracy.

References in corpus (1)

• Accelerating Dynamical Fermion Computations using the Rational Hybrid Monte Carlo (RHMC) Algorithm with Multiple Pseudofermion Fields

Cited by in corpus (6)

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