Computational Aspects of Complex Analysis

1. Front Matter

   Pages i-viii

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2. Outlines of Pade Approximation

   • Claude Brezinski

   Pages 1-50

3. Numerical Methods in Conformal Mapping

   • Dieter Gaier

   Pages 51-78

4. On Complex Rational Approximation

   • Martin H. Gutknecht

   Pages 79-101

5. On Complex Rational Approximation

   • Martin H. Gutknecht

   Pages 103-132

6. Topics in Computational Complex Analysis: I. Methods of Descent for Polynomial Equations

   • Peter Henrici

   Pages 133-147

7. Topics in Computational Complex Analysis: II. New Developments Concerning the Quotient-Difference Algorithm

   • Peter Henrici

   Pages 149-168

8. Topics in Computational Complex Analysis: III. The Asymptotic Behavior of Best Approximations to Analytic Functions on the Unit Disk

   • Peter Henrici

   Pages 169-191

9. Topics in Computational Complex Analysis: IV. The Lagrange-Bürmann Formula for Systems of Formal Power Series

   • Peter Henrici

   Pages 193-215

10. A Simplified Presentation of the Adamjan-Arov-Krein Approximation Theory

    • Jean Meinguet

    Pages 217-248

11. Fast Fourier Transform Algorithms with Applications

    • Gerhard Merz

    Pages 249-278

12. Error Analysis of Complex Arithmetic

    • F. W. J. Olver

    Pages 279-292

13. The Use of Green’s Boundary Formula in Potential Theory

    • George T. Symm

    Pages 293-308

14. Chebyshev Approximation on the Unit Disk

    • Lloyd N. Trefethen

    Pages 309-323

15. Calculations of Singularities for Solutions of Algebraic Differential Equations

    • Helmut Werner

    Pages 325-360

16. On the Use of a Class of Algebraic Mappings Techniques for Some Problems in Complex Analysis

    • David Y. Y. Yun

    Pages 361-377

17. Computer Algebra and Complex Analysis

    • David Y. Y. Yun

    Pages 379-393

18. Short Communications

    • M. C. de Bruin, A. Bultheel, L. Casasús, A. Cuyt, J. Della Dora, R. Farwig et al.

    Pages 395-414

19. Back Matter

    Pages 415-426

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The NATO Advanced study Institute (ASI) on "Computational Aspects of Complex Analysis" was held at Braunlage/Harz (Germany) from July 26 to August 6, 1982. These proceedings contain the invited lectures presented at this institute, the aim of which was to bring together scientists from pure and applied mathematics as well as computer scientists. The main topics were problems dealing with approximation and interpolation by polynomial and rational functions (in particular Pade approximation), numerical methods for the solution of algebraic equations and differential equations, the large field of conformal mapping, aspects of computer imple­ mentation of complex arithmetic and calculations based on complex variable techniques. The sessions on short communications not only provided a platform for the presentation of contributions by the participants of the ASI but also the opportunity to discuss the material more thoroughly, to bring up open problems and to point out the inter­ relationship of the above mentioned topics. Quite naturally the short communications grouped around the topics of the main lectures. The stimulating atmosphere caused many discussions to continue privately for hours. Even out of the social program there emanated two short communications by L. Wuytack and L. Trefethen, which are included at the end of these proceedings. We gratefully appreciate the support of the International Advisory Committee that was formed by L. Collatz, Germany, C. Brezinski, France, G. Golub, U.S.A., P. Henrici, Switzerland, J. van Hulzen, the Netherlands, O. Skovgaard, Denmark, I. Sneddon, United Kingdom, and J. Todd, U.S.A.

• Approximation
• Potential
• algorithms
• approximation theory
• calculus
• computer
• computer algebra
• numerical methods

• University of Bonn, West Germany

  H. Werner, H. J. Bünger

• Universitaire Instelling Antwerpen, Belgium

  L. Wuytack

• Jet Propulsion Laboraories, Pasadena, USA

  E. Ng

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