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Full Description
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.
Contents
Outlines of Padé Approximation.- Numerical Methods in Conformal Mapping.- On Complex Rational Approximation Part I: The Characterization Problem.- On Complex Rational Approximation Part II: The Carathéodory-Fejér Method.- Topics in Computational Complex Analysis I. Methods of Descent for Polynomial Equations.- Topics in Computational Complex Analysis II. New Developments Concerning the Quotient-Difference Algorithm.- Topics in Computational Complex analysis III. The Asymptotic Behavior of Best Approximations to Analytic Functions on the Unit Disk.- Topics in Computational Complex analysis IV. The Lagrange-Bürmann Formula for Systems of Formal Power Series.- A Simplified Presentation of the Adamjan-Arov-Krein Approximation Theory.- Fast Fourier Transform Algorithms with Applications.- Error Analysis of Complex Arithmetic.- The Use of Green's Boundary Formula in Potential Theory.- Chebyshev Approximation on the Unit Disk.- Calculations of Singularities for Solutions of Algebraic Differential Equations.- On the Use of a Class of Algebraic Mappings Techniques for Some Problems in Complex Analysis.- Computer Algebra and Complex Analysis.- Short Communications.- List of Participants.
