An extension of a Nevanlinna-Pick interpolation solver to cases including derivative constraints

This paper extends a previously proposed solver for scalar Nevanlinna-Pick interpolation problems with degree constraint to the ones including derivative constraints. The solver computes any real rational interpolant with a degree bound by solving an optimization problem of the same type as encountered in the problem without derivative constraint. A robust homotopy continuation method, previously devised by the second author for the problem without derivative constraint, can be applied to solve the new optimization problem.