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THE RKFIT ALGORITHM FOR NONLINEAR RATIONAL APPROXIMATION
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DOI：10.1137/15M1025426.png)
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Abstract
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The RKFIT algorithm outlined in [M. Berljafa and S. Ciittel, SIAM J. Matrix Anal. Appl., 36 (2015), pp. 894-916] 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 for root-finding. We also discuss similarities and differences between RKFIT and the popular vector fitting algorithm. A MATLAB implementation of RKFIT is provided, and numerical experiments, including the fitting of a multiple-input/multiple-output (MIMO) dynamical system and an optimization problem related to exponential integration, demonstrate its applicability.
Keywords:
nonlinear rational approximation
least squares
rational Krylov method
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