Circular centered forms for rational functions in several complex variables (Q1195397)

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.