Computational Methods and Function Theory

Proceedings of a Conference, held in Valparaíso, Chile, March 13–18, 1989

  • Editors
  • Stephan Ruscheweyh
  • Edward B. Saff
  • Luis C. Salinas
  • Richard S. Varga
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1435)

Table of contents

  1. Front Matter
    Pages I-VI
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  2. Open problems and conjectures in complex analysis
    Roger W. Barnard
    Pages 1-26
  3. A remarkable cubic mean iteration
    J. M. Borwein, P. B. Borwein
    Pages 27-31
  4. On the maximal range problem for slit domains
    Antonio Córdova Yévenes, Stephan Ruscheweyh
    Pages 33-44
  5. On bernstein type inequalities and a weighted chebyshev approximation problem on ellipses
    Roland Freund
    Pages 45-55
  6. Conformal mapping and Fourier-Jacobi approximations
    David M. Hough
    Pages 57-70
  7. Numerical solutions of the schiffer equation
    J. A. Hummel
    Pages 71-79
  8. Behavior of the lagrange interpolants in the roots of unity
    K. G. Ivanov, E. B. Saff
    Pages 81-87
  9. Orthogonal polynomials, chain sequences, three-term recurrence relations and continued fractions
    Lisa Jacobsen
    Pages 89-101
  10. On Thurston's formulation and proof of Andreev's theorem
    Al Marden, Burt Rodin
    Pages 103-115
  11. Hyperbolic geometry in spherically k-convex regions
    Diego Mejía, David Minda
    Pages 117-129
  12. The Bloch and Marden constants
    David Minda
    Pages 131-142
  13. On some analytic and computational aspects of two dimensional vortex sheet evolution
    O. F. Orellana
    Pages 143-154
  14. On the numerical performance of a domain decomposition method for conformal mapping
    N. Papamichael, N. S. Stylianopoulos
    Pages 155-169
  15. Planar harmonic mappings
    Glenn Schober
    Pages 171-176
  16. Extremal problems for non-vanishing Hp functions
    T. J. Suffridge
    Pages 177-190
  17. Some results on separate convergence of continued fractions
    W. J. Thron
    Pages 191-200
  18. Asymptotics for the zeros of the partial sums of ez. II
    R. S. Varga, A. J. Carpenter
    Pages 201-207
  19. Back Matter
    Pages 209-215
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About this book

Introduction

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.

Keywords

Complex analysis Maxima calculus differential equation extrema geometry maximum orthogonal polynomials

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0087892
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-52768-8
  • Online ISBN 978-3-540-47139-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book