Extremal Polynomials and Riemann Surfaces

Andrei Bogatyrev

ISBN 10: 364244332X / ISBN 13: 9783642443329

Editore: Springer Berlin Heidelberg Jun 2014, 2014

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This item is printed on demand - it takes 3-4 days longer - Neuware -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. 176 pp. Englisch. Codice articolo 9783642443329

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Titolo: Extremal Polynomials and Riemann Surfaces

Casa editrice: Springer Berlin Heidelberg Jun 2014

Data di pubblicazione: 2014

Legatura: Taschenbuch

Condizione: Neu

Descrizione articolo

Riassunto:

This book develops the classical Chebyshev's approach which gives analytical representation for the solution in terms of Riemann surfaces. It includes numerous problems, exercises, and illustrations.

Recensione:

From the reviews:

“This book develops the classical Chebyshev approach to optimization problems in polynomial spaces. This approach yields an analytical representation for the solution in terms of Riemann surfaces. The text includes numerous problems, exercises, and illustrations. ... In this book, methods from various areas of mathematics are used. ... It has more than 150 pages throughout which the author makes a lot of effort to give as many results as possible, and yet provide lots of details to make the reading easier.” (Konstantin Malyutin, Zentralblatt MATH, Vol. 1252, 2012)