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Andrei Bogatyrev 
Extremal Polynomials and Riemann Surfaces 

Wsparcie

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.​

€53.49
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Spis treści

1 Least deviation problems.- 2 Chebyshev representation of polynomials.- 3 Representations for the moduli space.- 4 Cell decomposition of the moduli space.- 5 Abel’s equations.- 6 Computations in moduli spaces.- 7 The problem of the optimal stability polynomial.- Conclusion.- References.

O autorze

The author is working in the field of complex analysis, Riemann surfaces and moduli, optimization of numerical algorithms, mathematical physics. He was awarded the S.Kowalewski Prize in 2009 by the Russian Academy of Sciences
Język Angielski ● Format PDF ● Strony 150 ● ISBN 9783642256349 ● Rozmiar pliku 2.9 MB ● Tłumacz Nikolai Kruzhilin ● Wydawca Springer Berlin ● Miasto Heidelberg ● Kraj DE ● Opublikowany 2012 ● Do pobrania 24 miesięcy ● Waluta EUR ● ID 2477304 ● Ochrona przed kopiowaniem Społeczny DRM

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