Circular centered forms for rational functions in several complex variables
type: Item
instance of: scholarly article
title: Circular centered forms for rational functions in several complex variables
zbMATH Open document ID: 0772.65036
DOI: 10.1016/0377-0427(92)90141-J
author: Qun Lin
author: J. Rokne
published in: Journal of Computational and Applied Mathematics
publication date: 1992-10-26T00:00:00Z
review text: This paper continues the second author's work in complex interval analysis. [See \textit{J. Rokne}, J. Comput. Appl. Math. 17, 309-327 (1987; Zbl 0614.65051), and \textit{P. Bao, J. Rokne}, Acta Appl. Math. 16, No. 3, 261-280 (1989; Zbl 0687.65018)]. Let \(f: \mathbb{C}^ n \to \mathbb{C}\) be a rational function of \(n\) complex variables. Let \(Z = \langle c,r\rangle\) denote a disk-shaped subset in \(\mathbb{C}^ n\), characterized by the ``center'' \(c\in \mathbb{C}^ n\) and the ``radius'' \(r \in \mathbb{R}^ n\). Define \(f(Z):=\{f(z)| z\in Z\}\). One basic aim of interval analysis is the construction of a disk \(D\) in \(\mathbb{C}\) that contains the set \(f(Z)\). The authors present explicit formulas for such disks \(D\), in particular they provide ``centered forms'', where the center of \(D\) is \(f(c)\). Furthermore, the authors prove interesting convergence properties of their centered forms. The paper is purely theoretical, no numerical results are reported.
reviewed by: Herbert Fischer
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 69598
zbMATH Keywords: circular arithmetic
zbMATH Keywords: centered forms
zbMATH Keywords: complex interval analysis
zbMATH Keywords: rational function
zbMATH Keywords: convergence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 69598