A new formal approach to the rational interpolation problem
The authors present a new algorithm for the construction of a rational function \(n(z)/d(z)\) satisfying the interpolation conditions \(n(z_ i)/d(z_ i)=l_ i/m_ i\), where \(z_ i\), \(i=1,2,\dots,p\), are the interpolation points and \(l_ i/m_ i\) the corresponding function values. This recursive algorithm does not require a recordering of the data points, thus allowing to add more interpolation data during the computation. Moreover, confluent interpolation points, poles and \(\infty\) may be considered as interpolation points. Not only the specific solution of the problem is given but also a parametrization of all solutions. A linear algebra interpretation of the problem shows that the algorithm can be used to handle a specific class of structured matrices.
scientific article; zbMATH DE number 118302
scientific article