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Extremal Polynomials and Riemann Surfaces
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Catalogue Information
Field name
Details
Dewey Class
515.9
Title
Extremal Polynomials and Riemann Surfaces ([Ebook]) / by Andrei Bogatyrev.
Author
Bogatyrev, Andrei
Other name(s)
SpringerLink (Online service)
Publication
Berlin, Heidelberg : Springer
, 2012.
Physical Details
XXV, 150 pages, 47 illus. : online resource.
Series
Springer monographs in mathematics
1439-7382
ISBN
9783642256349
Summary Note
The problems of conditional optimization of the uniform (or C-) norm for polynomials and rational functions arise in various branches of science and technology. Their numerical solution is notoriously difficult in case of high degree functions. The book develops the classical Chebyshev's approach which gives analytical representation for the solution in terms of Riemann surfaces. The techniques born in the remote (at the first glance) branches of mathematics such as complex analysis, Riemann surfaces and TeichmÜller theory, foliations, braids, topology are applied to approximation problems. The key feature of this book is the usage of beautiful ideas of contemporary mathematics for the solution of applied problems and their effective numerical realization. This is one of the few books' where the computational aspects of the higher genus Riemann surfaces are illuminated. Effective work with the moduli spaces of algebraic curves provides wide opportunities for numerical experiments in mathematics and theoretical physics.:
Contents note
1 Least deviation problems -- 2 Chebyshev representation of polynomials -- 3 Representations for the moduli space -- 4 Cell decomposition of the moduli space -- 5 Abelâs equations -- 6 Computations in moduli spaces -- 7 The problem of the optimal stability polynomial -- Conclusion -- References.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site
http://dx.doi.org/10.1007/978-3-642-25634-9
Links to Related Works
Subject References:
Appl.Mathematics/Computational Methods of Engineering
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Approximations and Expansions
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Engineering mathematics
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Functions of complex variables
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Global analysis
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Global Analysis and Analysis on Manifolds
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Manifolds (Mathematics)
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Numerical Analysis
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Numerical and Computational Physics
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Authors:
Bogatyrev, Andrei
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Corporate Authors:
SpringerLink (Online service)
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Series:
Springer monographs in mathematics
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Classification:
515.9
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515.9 (DDC 23)
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