Approximation of conformal mappings of annular regions |
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| Authors: | N. Papamichael I.E. Pritsker E.B. Saff N.S. Stylianopoulos |
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| Affiliation: | (1) Department of Mathematics and Statistics, University of Cyprus, P.O. Box 537, Nicosia, Cyprus; e-mail: nickp@pythagoras.mas.ucy.ac.cy , CY;(2) Department of Mathematics and Computer Science, Kent State University, Kent, OH 44240, USA; e-mail: pritsker@mcs.kent.edu , US;(3) Institute for Constructive Mathematics, Department of Mathematics, University of South Florida, 4202 East Fowler Ave., Tampa, FL 33620, USA; e-mail: esaff@math.usf.edu , US;(4) Department of Mathematics and Statistics, University of Cyprus, P.O. Box 537, Nicosia, Cyprus; e-mail: nikos@pythagoras.mas.ucy.ac.cy , CY |
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| Abstract: | Summary. In this paper we examine the convergence rates in an adaptive version of an orthonormalization method for approximating the conformal mapping of an annular region onto a circular annulus. In particular, we consider the case where has an analytic extension in compl() and, for this case, we determine optimal ray sequences of approximants that give the best possible geometric rate of uniform convergence. We also estimate the rate of uniform convergence in the case where the annular region has piecewise analytic boundary without cusps. In both cases we also give the corresponding rates for the approximations to the conformal module of . Received February 2, 1996 |
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| Keywords: | Mathematics Subject Classification (1991): 30C30 65E05 41A20 |
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