Convergence rates for inverse-free rational approximation of matrix functions

This article deduces geometric convergence rates for approxi-mating matrix functions via inverse-free rational Krylov meth-ods. In applications one frequently encounters matrix func-tions such as the matrix exponential or matrix logarithm; often the matrix under consideration is too large to compute the matrix function directly, and Krylov subspace methods are used to determine a reduced problem. If many evaluations of a matrix function of the form f(A)vwith a large matrix Aare required, then it may be advantageous to determine a reduced problem using rationalKrylov subspaces. These methods may give more accurate approximations of f(A)vwith subspaces of smaller dimension than standard Krylov subspace meth-ods. Unfortunately, the system solves required to construct an orthogonal basis for a rational Krylov subspace may cre-ate numerical difficulties and/or require excessive computingpublisher: Elsevier articletitle: Convergence rates for inverse-free rational approximation of matrix functions journaltitle: Linear Algebra and its Applications articlelink: http://dx.doi.org/10.1016/j.laa.2016.08.029 content_type: article copyright: © 2016 Elsevier Inc. All rights reserved.status: publishe