Computational Methods and Function Theory: Proceedings of a Conference, held in Valparaíso, Chile, March 13–18, 1989

Roger W. Barnard (auth.), Stephan Ruscheweyh, Edward B. Saff, Luis C. Salinas, Richard S. Varga (eds.)9783540527688, 3-540-52768-0, 0387527680

The volume is devoted to the interaction of modern scientific computation and classical function theory. Many problems in pure and more applied function theory can be tackled using modern computing facilities: numerically as well as in the sense of computer algebra. On the other hand, computer algorithms are often based on complex function theory, and dedicated research on their theoretical foundations can lead to great enhancements in performance. The contributions – original research articles, a survey and a collection of problems – cover a broad range of such problems.

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Table of contents :
Open problems and conjectures in complex analysis….Pages 1-26
A remarkable cubic mean iteration….Pages 27-31
On the maximal range problem for slit domains….Pages 33-44
On bernstein type inequalities and a weighted chebyshev approximation problem on ellipses….Pages 45-55
Conformal mapping and Fourier-Jacobi approximations….Pages 57-70
Numerical solutions of the schiffer equation….Pages 71-79
Behavior of the lagrange interpolants in the roots of unity….Pages 81-87
Orthogonal polynomials, chain sequences, three-term recurrence relations and continued fractions….Pages 89-101
On Thurston’s formulation and proof of Andreev’s theorem….Pages 103-115
Hyperbolic geometry in spherically k -convex regions….Pages 117-129
The Bloch and Marden constants….Pages 131-142
On some analytic and computational aspects of two dimensional vortex sheet evolution….Pages 143-154
On the numerical performance of a domain decomposition method for conformal mapping….Pages 155-169
Planar harmonic mappings….Pages 171-176
Extremal problems for non-vanishing H p functions….Pages 177-190
Some results on separate convergence of continued fractions….Pages 191-200
Asymptotics for the zeros of the partial sums of e z . II….Pages 201-207