A new algorithm for meromorphic Nevanlinna-Pick interpolation
type: Item
instance of: scholarly article
title: A new algorithm for meromorphic Nevanlinna-Pick interpolation
zbMATH Open document ID: 1080.65008
author: Christer Glader
author: Mikael Lindström
published in: Numerische Mathematik
publication date: 2005-04-14T00:00:00Z
review text: Let \(H_0^\infty\) be the space of all bounded analytic functions in the unit disk \(D\). The set of all functions \(f(z)/p(z)\), where \(p(z)=(z-z_1)...(z-z_k)\), \(z_i\in D\) and \(f\in H_0^\infty\), is denoted by \(H_k^\infty\). Problem I: Let \(z_j\in D\), \(w_j\in {\mathbb{C}}\), \(j=1,...,n\), and \(0\leq k <n\). Find \(f\in H_k^\infty\) such that \(f(z_i)=w_i\), \(1\leq i\leq n\) and \(\| f\| _\infty\) is minimized. Assumption A: Given the interpolation data Problem I has a solution in each class \(H^\infty_k\), \(0<k<n\). The main result of this paper (Theorem 2.3) gives a detailed description of the rational function which is the unique solution of Problem I under Assumption A. The authors present an algorithm which is derived from Theorem 2.3 for the numerical solution of Problem I. Two examples have been chosen to illustrate the power of this approach.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 30D50
Mathematics Subject Classification ID: 30E05
zbMATH DE Number: 2156013
zbMATH Keywords: Nevanlinna-Pick interpolation problem
zbMATH Keywords: rational interpolation
zbMATH Keywords: numerical examples
zbMATH Keywords: bounded analytic functions
zbMATH Keywords: algorithm
reviewed by: J. Illán
MaRDI profile type: Publication
full work available at URL: s00211-005-0584-7
OpenAlex ID: W2007155059
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DOI: 10.1007/S00211-005-0584-7
description: scientific article; zbMATH DE number 2156013