Computational Methods and Function Theory [electronic resource] : Proceedings of a Conference, held in Valparaíso, Chile, March 13–18, 1989 / edited by Stephan Ruscheweyh, Edward B. Saff, Luis C. Salinas, Richard S. Varga.

Open problems and conjectures in complex analysis -- A remarkable cubic mean iteration -- On the maximal range problem for slit domains -- On bernstein type inequalities and a weighted chebyshev approximation problem on ellipses -- Conformal mapping and Fourier-Jacobi approximations -- Numerical solutions of the schiffer equation -- Behavior of the lagrange interpolants in the roots of unity -- Orthogonal polynomials, chain sequences, three-term recurrence relations and continued fractions -- On Thurston's formulation and proof of Andreev's theorem -- Hyperbolic geometry in spherically k-convex regions -- The Bloch and Marden constants -- On some analytic and computational aspects of two dimensional vortex sheet evolution -- On the numerical performance of a domain decomposition method for conformal mapping -- Planar harmonic mappings -- Extremal problems for non-vanishing H p functions -- Some results on separate convergence of continued fractions -- Asymptotics for the zeros of the partial sums of ez. II.

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.