The RKFIT algorithm for nonlinear rational approximation

Mario Berljafa, Stefan Güttel

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    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.
    Original languageEnglish
    Pages (from-to)A2049-A2071
    Number of pages23
    JournalSIAM Journal on Scientific Computing
    Issue number5
    Early online date19 Sept 2017
    Publication statusPublished - 2017


    • nonlinear rational approximation
    • Least squares
    • rational Krylov method


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