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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
Publication	, 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 . Approximations and Expansions . Engineering mathematics . Functions of complex variables . Global analysis . Global Analysis and Analysis on Manifolds . Manifolds (Mathematics) . Numerical Analysis . Numerical and Computational Physics . Authors: Bogatyrev, Andrei . Corporate Authors: SpringerLink (Online service) . Series: Springer monographs in mathematics . Classification: 515.9 . 515.9 (DDC 23) .

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Extremal Polynomials and Riemann Surfaces

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