Browsing by Author "Saff, E. B."
Now showing items 1-15 of 15
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Article
Approximation of conformal mappings of annular regions
Papamichael, Nicolas; Pritsker, I. E.; Saff, E. B.; Stylianopoulos, Nikos S. (1997)In this paper we examine the convergence rates in an adaptive version of an orthonormalization method for approximating the conformal mapping f of an annular region A onto a circular annulus. In particular, we consider the ...
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Article
Asymptotic behaviour of zeros of Bieberbach polynomials
Papamichael, Nicolas; Saff, E. B.; Gong, J. (1991)Let Ω be a simply-connected domain in the complex plane and let πn denote the nth-degree Bieberbach polynomial approximation to the conformal map f of Ω onto a disc. In this paper we investigate the asymptotic behaviour ...
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Asymptotic Zero Distribution of Laurent-Type Rational Functions
Papamichael, Nicolas; Pritsker, I. E.; Saff, E. B. (1997)We study convergence and asymptotic zero distribution of sequences of rational functions with fixed location of poles that approximate an analytic function in a multiply connected domain. Although the study of zero ...
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Article
Asymptotics for Hessenberg Matrices for the Bergman Shift Operator on Jordan Regions
Saff, E. B.; Stylianopoulos, Nikos S. (2014)Let G be a bounded Jordan domain in the complex plane. The Bergman polynomials {pn}n=0∞ of G are the orthonormal polynomials with respect to the area measure over G. They are uniquely defined by the entries of an infinite ...
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Article
Bergman orthogonal polynomials on an archipelago
Gustafsson, B.; Putinar, M.; Saff, E. B.; Stylianopoulos, Nikos S. (2008)Growth estimates for orthogonal polynomials with respect to area measure (Bergman polynomials) over the union of finitely many Jordan regions with piecewise smooth boundary are obtained by a careful investigation of the ...
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Article
Bergman polynomials on an archipelago: Estimates, zeros and shape reconstruction
Gustafsson, B.; Putinar, M.; Saff, E. B.; Stylianopoulos, Nikos S. (2009)Growth estimates of complex orthogonal polynomials with respect to the area measure supported by a disjoint union of planar Jordan domains (called, in short, an archipelago) are obtained by a combination of methods of ...
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Book
Computational methods and function theory 1997 proceedings of the Third CMFT Conference, 13-17 October 1997, Nicosia, Cyprus
Papamichael, Nicolas; Ruscheweyh, Stephan; Saff, E. B. (World Scientific, 1999)
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L2-approximations of power and logarithmic functions with applications to numerical conformal mapping
Maymeskul, V. V.; Saff, E. B.; Stylianopoulos, Nikos S. (2002)For a bounded Jordan domain G with quasiconformal boundary L, two-sided estimates are obtained for the error in best L2(G) polynomial approximation to functions of the form (z - τ)β, β > -1, and (z - τ)m logl(z - τ), m > ...
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Article
Local behaviour of the error in the Bergman kernel method for numerical conformal mapping
Papamichael, Nicolas; Saff, E. B. (1993)Let Ω be a simply-connected domain in the complex plane, let ζ ε{lunate} Ω and let K(z, ζ) denote the Bergman kernel function of Ω with respect to ζ. Also, let Kn(z, ζ) denote the nth-degree polynomial approximation to ...
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Article
On finite-term recurrence relations for Bergman and Szego{double acute} polynomials
Baratchart, L.; Saff, E. B.; Stylianopoulos, Nikos S. (2012)With the aid of Havin's Lemma (which we generalize) we prove that polynomials orthogonal over the unit disk with respect to certain weighted area measures (Bergman polynomials) cannot satisfy a finite-term recurrence ...
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On the zeros of asymptotically extremal polynomial sequences in the plane
Saff, E. B.; Stylianopoulos, Nikos S. (2015)Let E be a compact set of positive logarithmic capacity in the complex plane and let {Pn(z)}1∞ be a sequence of asymptotically extremal monic polynomials for E in the sense that lim supn→∞{norm of matrix}Pn{norm of ...
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Orthogonal polynomials for area-type measures and image recovery
Saff, E. B.; Stahl, H.; Stylianopoulos, Nikos S.; Totik, V. (2015)Let G be a finite union of disjoint and bounded Jordan domains in the complex plane, let K be a compact subset of G, and consider the set G∗ obtained from G by removing K
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Article
Preface
Papamichael, Nicolas; Saff, E. B. (1993)
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Article
Relative asymptotics of orthogonal polynomials for perturbed measures
Saff, E. B.; Stylianopoulos, Nikos (2018)
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Article
Zero distribution of Bergman orthogonal polynomials for certain planar domains
Levin, A. L.; Saff, E. B.; Stylianopoulos, Nikos S. (2003)Let G be a simply connected domain in the complex plane bounded by a closed Jordan curve L and let Pn, n ≥ 0, be polynomials of respective degrees n = 0, 1,... that are orthonormal in G with respect to the area measure ...