The RKFIT algorithm for nonlinear rational approximation

The RKFIT algorithm outlined in [M. Berljafa and S. Guttel, Generalized rational Krylov decompositions with an application to rational approximation, SIAM J. Matrix Anal. Appl., 2015] is a Krylov-based approach for solving nonlinear rational least squares problems. This paper puts RKFIT into a general framework, allowing for its extension to nondiagonal rational approximants and a family of approximants sharing a common denominator. Furthermore, we derive a strategy for the degree reduction of the approximants, as well as methods for their conversion to partial fraction form, for the efficient evaluation, and root-finding. We also discuss commons and differences of RKFIT and the popular vector fitting algorithm. A MATLAB implementation of RKFIT is provided and numerical experiments, including the fitting of a MIMO dynamical system
and an optimization problem related to exponential integration, demonstrate its applicability.