ON THE SCALAR RATIONAL INTERPOLATION PROBLEM

A new technique is derived for determining a parametrization of all mi nimal complexity rational functions a(x)/b(x) interpolating an arbitra ry sequence of points. Complexity is measured in terms of max{deg(a),d eg(b) + r} where r is an arbitrary integer (so that r = 0 corresponds to the McMillan degree). Our construction uses Grobner bases of submod ules of the free module of rank 2 over the polynomial ring in one vari able and extends previous work on the key equation of error control co ding theory.