Document Type

Article

Department/Program

Mathematics

Journal Title

Journal of Computational and Applied Mathematics

Pub Date

2012

Volume

236

Issue

13

First Page

3123

Abstract

For the Nevanlinna-Pick interpolation problem with n interpolation conditions (interior and boundary), we construct a family of rational solutions of degree at most n - 1. We also establish necessary and sufficient conditions for the existence and the uniqueness of a solution with the minimally possible H-infinity-norm and construct a family of minimal-norm rational solutions of degree at most n - 1 in the indeterminate case. Finally, we supplement a result of Ruscheweyh and Jones showing that in case the interpolation nodes and the target values are all unimodular, any rational solution of degree at most n - 1 is necessarily a finite Blaschke product. (C) 2012 Elsevier B.V. All rights reserved.

DOI

10.1016/j.cam.2012.02.009

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