On a diagonal Padé approximation in two complex variables
type: Item
instance of: scholarly article
title: On a diagonal Padé approximation in two complex variables
zbMATH Open document ID: 1016.65006
author: Mihai Putinar
published in: Numerische Mathematik
publication date: 2002-12-01T00:00:00Z
review text: The motivation for the present paper is a special reconstruction algorithm of planar shapes [cf. \textit{B. Gustafsson, C. He, P. Milanfar}, and \textit{M. Putinar}, Inverse Prob. 16, No.~4, 1053-1070 (2000; Zbl 0959.44010)]. The reconstruction problem leads via the approximation by rational functions of transfer functions in linear control theory [\textit{C. Foiaş, A. E. Frazho}, The commutant lifting approach to interpolation problems. Birkhäuser Verlag, Basel, Boston (1990; Zbl 0718.47010)] to a Padé approximation approach of a class of power series in two variables. The problem is then reduced to a Padé approximation problem in one variable [\textit{G. A. Baker, jun.}, and \textit{P. Graves-Morris}, Padé approximants. Part I: Basic theory (1981; Zbl 0468.30032), Part II: Extensions and applications (1981; Zbl 0468.30033); \textit{A. Cuyt}, J. Comput. Appl. Math. 105, No.~1-2, 25-50 (1999; Zbl 0945.41012)]. The convergence of the approximation process is derived from operator theory which governs the whole argumentation.
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 92C55
zbMATH DE Number: 1837416
zbMATH Keywords: reconstruction algorithm
zbMATH Keywords: rational functions
zbMATH Keywords: Padé approximation
zbMATH Keywords: convergence
reviewed by: Walter Schempp
MaRDI profile type: Publication
full work available at URL: s002110100357
OpenAlex ID: W4234145707
DOI: 10.1007/S002110100357
description: scientific article; zbMATH DE number 1837416