Summary
Vector Fitting (VF) is an iterative technique to construct rational approximations based on multiple frequency domain samples, introduced by Gustavsen and Semlyen [1, 3]. VF is nowadays widely investigated and used in the Power Systems and Microwave Engineering communities. Numerical experiments show that VF has favorable convergence properties. However, so far, no theoretical proof for its convergence, or conditions to guarantee convergence, have been published. This paper gives a description of a general iterative Least-Squares framework for rational approximation and shows that VF fits into this framework.
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References
Bjorn Gustavsen and Adam Semlyen. Rational approximation of frequency domain responses by Vector Fitting. IEEE Transactions on Power Delivery, 14(3):1052–1061, 1999.
C. K. Sanathanan and J. Koerner. Transfer function synthesis as a ratio of two complex polynomials. IEEE trans. Automat. Contr., 8:56–58, 1963.
A. Semlyen and B. Gustavsen. Vector Fitting by pole relocation for the state equation approximation of nonrational transfer matrices. Circuits and systems: Analog and Digital signal processing, 19(6):549–566, 2000.
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© 2006 Springer-Verlag Berlin Heidelberg
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Hendrickx, W., Deschrijver, D., Dhaene, T. (2006). Some Remarks on the Vector Fitting Iteration. In: Di Bucchianico, A., Mattheij, R., Peletier, M. (eds) Progress in Industrial Mathematics at ECMI 2004. Mathematics in Industry, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28073-1_15
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DOI: https://doi.org/10.1007/3-540-28073-1_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28072-9
Online ISBN: 978-3-540-28073-6
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