Padé-type approximations to the resolvent of fractional powers of operators
For researchers in numerical analysis and scientific computing, this work offers practical error bounds for rational Krylov methods applied to fractional operators.
The paper develops reliable pole selection for rational approximation of the resolvent of fractional powers of operators, providing quantitatively accurate error estimates validated by numerical examples.
We study a reliable pole selection for the rational approximation of the resolvent of fractional powers of operators in both the finite and infinite dimensional setting. The analysis exploits the representation in terms of hypergeometric functions of the error of the Padé approximation of the fractional power. We provide quantitatively accurate error estimates that can be used fruitfully for practical computations. We present some numerical examples to corroborate the theoretical results. The behavior of the rational Krylov methods based on this theory is also presented.