We consider here the problem of constructing a general recursive algorithm to interpolate a given set of data with a rational function. While many algorithms of this kind already exists, they are either providing non minimal-degree solutions (like the Schur algorithm), or exhibit jumps in the degree of the interpolants (or of the partial realization, as the problem is called when the interpolation is at infinity, see Rissanen and Gragg-Lindquist). By imbedding the solution into a larger set of interpolants, we show that the increase in the degree of this representation always equals the increase in the length of the data. We focus here on the interpolation problem at zero
On scalar recursive interpolation, partial realization and related problems
2015
Abstract
We consider here the problem of constructing a general recursive algorithm to interpolate a given set of data with a rational function. While many algorithms of this kind already exists, they are either providing non minimal-degree solutions (like the Schur algorithm), or exhibit jumps in the degree of the interpolants (or of the partial realization, as the problem is called when the interpolation is at infinity, see Rissanen and Gragg-Lindquist). By imbedding the solution into a larger set of interpolants, we show that the increase in the degree of this representation always equals the increase in the length of the data. We focus here on the interpolation problem at zeroI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
