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Extremal Polynomials and Riemann Surfaces von Bogatyrev, Andrei (eBook)

  • Erscheinungsdatum: 31.05.2012
  • Verlag: Springer-Verlag
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Extremal Polynomials and Riemann Surfaces

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.

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


    Format: PDF
    Kopierschutz: AdobeDRM
    Seitenzahl: 150
    Erscheinungsdatum: 31.05.2012
    Sprache: Englisch
    ISBN: 9783642256349
    Verlag: Springer-Verlag
    Größe: 3209 kBytes
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