Using polynomial interpolation, along with structural properties of the family of rational positive real functions, we here show that a set of m nodes in the open left half of the complex plane, can always be mapped to anywhere in the complex plane by rational positive real functions whose degree is at most m. Moreover we introduce an easy-to-find parametrization in R2m+3 of a large subset of these interpolating functions.
D. Alpay, I. Lewkowicz, “Wrong” side interpolation by positive real rational functions, Linear Algebra Appl. (2017), http://dx.doi.org/10.1016/j.laa.2017.09.016
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Available for download on Friday, September 20, 2019