Minimal degree rational unimodular interpolation on the unit circle

Abstract

We consider an interpolation problem with $n$ distinct nodes $z_1,\ldots,z_n$ and $n$ interpolation values $w_1,\ldots,w_n$, all on the complex unit circle, and seek interpolants $b(z)$ of minimal degree in the class consisting of ratios of finite Blaschke products. The focus is on the so-called damaged cases where the interpolant of minimal degree is non-uniquely determined. This paper is a continuation of the work in Glader [Comput. Methods Funct. Theory, 6 (2006), pp. 481–492], which treated the uniquely solvable fragile and elastic cases.

Full Text (PDF) [260 KB]

Key words

rational interpolation, Blaschke product, Nevanlinna parametrization

30D50, 35E05

< Back