Abstract
A new technique is derived for determining a parametrization of all minimal complexity rational functionsa(x)/b(x) interpolating an arbitrary sequence of points. Complexity is measured in terms of max{deg(a), deg(b) +r } wherer is an arbitrary integer (so thatr=0 corresponds to the McMillan degree). Our construction uses Gröbner bases of submodules of the free module of rank 2 over the polynomial ring in one variable and extends previous work on the key equation of error control coding theory.
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Financial support from the Faculty of Arts, University College Cork, is gratefully acknowledged.
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Fitzpatrick, P. On the scalar rational interpolation problem. Math. Control Signal Systems 9, 352–369 (1996). https://doi.org/10.1007/BF01211856
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DOI: https://doi.org/10.1007/BF01211856