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.