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Extremal Polynomials and Riemann Surfaces

Extremal Polynomials and Riemann Surfaces
Catalogue Information
Field name Details
Dewey Class 515.9
Title Extremal Polynomials and Riemann Surfaces (EB) / 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
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