Extremal Polynomials and Riemann Surfaces

  • Andrei Bogatyrev

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Andrei Bogatyrev
    Pages 1-13
  3. Andrei Bogatyrev
    Pages 15-27
  4. Andrei Bogatyrev
    Pages 29-52
  5. Andrei Bogatyrev
    Pages 53-72
  6. Andrei Bogatyrev
    Pages 73-88
  7. Andrei Bogatyrev
    Pages 89-114
  8. Andrei Bogatyrev
    Pages 115-134
  9. Back Matter
    Pages 135-150

About this book

Introduction

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.​

Keywords

Pell-Abel equation Riemann surface Schottky model extremal polynomials least deviation problems

Authors and affiliations

  • Andrei Bogatyrev
    • 1
  1. 1.of the Russian Acad. SciencesInstitute of Numerical MathematicsMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-25634-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-25633-2
  • Online ISBN 978-3-642-25634-9
  • Series Print ISSN 1439-7382
  • About this book