Ebook: Computational Aspects of Complex Analysis: Proceedings of the NATO Advanced Study Institute held at Braunlage, Harz, Germany, July 26 – August 6, 1982
- Tags: Numeric Computing, Theoretical Mathematical and Computational Physics
- Series: NATO Advanced Study Institutes Series 102
- Year: 1983
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-viii
Outlines of Pade Approximation....Pages 1-50
Numerical Methods in Conformal Mapping....Pages 51-78
On Complex Rational Approximation....Pages 79-101
On Complex Rational Approximation....Pages 103-132
Topics in Computational Complex Analysis: I. Methods of Descent for Polynomial Equations....Pages 133-147
Topics in Computational Complex Analysis: II. New Developments Concerning the Quotient-Difference Algorithm....Pages 149-168
Topics in Computational Complex Analysis: III. The Asymptotic Behavior of Best Approximations to Analytic Functions on the Unit Disk....Pages 169-191
Topics in Computational Complex Analysis: IV. The Lagrange-B?rmann Formula for Systems of Formal Power Series....Pages 193-215
A Simplified Presentation of the Adamjan-Arov-Krein Approximation Theory....Pages 217-248
Fast Fourier Transform Algorithms with Applications....Pages 249-278
Error Analysis of Complex Arithmetic....Pages 279-292
The Use of Green’s Boundary Formula in Potential Theory....Pages 293-308
Chebyshev Approximation on the Unit Disk....Pages 309-323
Calculations of Singularities for Solutions of Algebraic Differential Equations....Pages 325-360
On the Use of a Class of Algebraic Mappings Techniques for Some Problems in Complex Analysis....Pages 361-377
Computer Algebra and Complex Analysis....Pages 379-393
Short Communications....Pages 395-414
Back Matter....Pages 415-426
Content:
Front Matter....Pages i-viii
Outlines of Pade Approximation....Pages 1-50
Numerical Methods in Conformal Mapping....Pages 51-78
On Complex Rational Approximation....Pages 79-101
On Complex Rational Approximation....Pages 103-132
Topics in Computational Complex Analysis: I. Methods of Descent for Polynomial Equations....Pages 133-147
Topics in Computational Complex Analysis: II. New Developments Concerning the Quotient-Difference Algorithm....Pages 149-168
Topics in Computational Complex Analysis: III. The Asymptotic Behavior of Best Approximations to Analytic Functions on the Unit Disk....Pages 169-191
Topics in Computational Complex Analysis: IV. The Lagrange-B?rmann Formula for Systems of Formal Power Series....Pages 193-215
A Simplified Presentation of the Adamjan-Arov-Krein Approximation Theory....Pages 217-248
Fast Fourier Transform Algorithms with Applications....Pages 249-278
Error Analysis of Complex Arithmetic....Pages 279-292
The Use of Green’s Boundary Formula in Potential Theory....Pages 293-308
Chebyshev Approximation on the Unit Disk....Pages 309-323
Calculations of Singularities for Solutions of Algebraic Differential Equations....Pages 325-360
On the Use of a Class of Algebraic Mappings Techniques for Some Problems in Complex Analysis....Pages 361-377
Computer Algebra and Complex Analysis....Pages 379-393
Short Communications....Pages 395-414
Back Matter....Pages 415-426
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