Computing function of large matrices by a preconditioned rational Krylov method

Rational Krylov methods are a powerful alternative for computing the product of a function of a large matrix times a given vector. However, the creation of the underlying rational subspaces requires solving sequences of large linear systems, a delicate task that can require intensive computational resources and should be monitored to avoid the creation of subspace different to those required. We propose the use of robust preconditioned iterative techniques to speedup the underlying process. We also discuss briefly how the inexact solution of these linear systems can affect the computed subspace. A preliminary test approximating a fractional power of the Laplacian matrix is included.