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Extremal Polynomials and Riemann Surfaces (Springer Monographs in Mathematics)

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Extremal Polynomials and Riemann Surfaces (Springer Monographs in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

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

Synopsis:

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.

About the Author

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

Table of Contents

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.

Product Details

ISBN:
9783642256332
Author:
Bogatyrev, Andrei
Publisher:
Springer
Author:
Kruzhilin, Nikolai
Subject:
Mathematical Analysis
Subject:
Pell-Abel equation
Subject:
Riemann surface
Subject:
Schottky model
Subject:
extremal polynomials
Subject:
least deviation problems
Subject:
Functions of a complex variable.
Subject:
Approximations and Expansions
Subject:
Numerical analysis
Subject:
Global Analysis and Analysis on Manifolds
Subject:
Numerical and Computational Physics
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
Mathematics-Applied
Copyright:
Edition Description:
2012
Series:
Springer Monographs in Mathematics
Publication Date:
20120331
Binding:
HARDCOVER
Language:
English
Pages:
175
Dimensions:
235 x 155 mm

Related Subjects

Health and Self-Help » Health and Medicine » Medical Specialties
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Introduction
Science and Mathematics » Mathematics » Numeric Analysis
Science and Mathematics » Physics » General
Science and Mathematics » Physics » Math

Extremal Polynomials and Riemann Surfaces (Springer Monographs in Mathematics) Used Hardcover
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Product details 175 pages Springer - English 9783642256332 Reviews:
"Synopsis" by , 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.
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