Gröbner basis solutions of constrained interpolation problems (Q1611921)

A general algorithm based upon a recursive Gröbner basis and applicable to a wide range of constrained interpolation problems is presented. Thus, in Section 2 some preliminary results and notations on Gröbner bases are given. Then, in Section 3, the general algorithm is presented, while Section 4 is devoted to a discussion on degree constraints since many problems arising in practice further constrain the required solutions by imposing limits on their degrees. As an application of this general algorithm, in Section 5 M-Padé approximation problems are considered. Finally, in Section 6, specific problems concerning error-correcting codes in list-decoding and soft-decision decoding are also dealt with.