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|a 9783642256349
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|a Bogatyrev, Andrei
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| 245 |
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|a Extremal Polynomials and Riemann Surfaces
|h Elektronische Ressource
|c by Andrei Bogatyrev
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| 250 |
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|a 1st ed. 2012
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2012, 2012
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| 300 |
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|a XXVI, 150 p
|b online resource
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|a 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
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| 653 |
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|a Engineering mathematics
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| 653 |
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|a Numerical Analysis
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| 653 |
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|a Functions of complex variables
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| 653 |
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|a Approximations and Expansions
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| 653 |
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|a Functions of a Complex Variable
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| 653 |
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|a Mathematical physics
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| 653 |
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|a Numerical analysis
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| 653 |
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|a Engineering / Data processing
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| 653 |
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|a Manifolds (Mathematics)
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| 653 |
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|a Approximation theory
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| 653 |
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|a Theoretical, Mathematical and Computational Physics
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| 653 |
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|a Global analysis (Mathematics)
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| 653 |
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|a Mathematical and Computational Engineering Applications
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| 653 |
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|a Global Analysis and Analysis on Manifolds
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
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|a Springer Monographs in Mathematics
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| 028 |
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|a 10.1007/978-3-642-25634-9
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| 856 |
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|u https://doi.org/10.1007/978-3-642-25634-9?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 515.9
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| 520 |
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|a 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
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