Extremal Polynomials and Riemann Surfaces

• Main Author: Bogatyrev, Andrei (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Approximation theory.; Functions of complex variables.; Global analysis (Mathematics).; Manifolds (Mathematics).; Numerical analysis.; Physics.; Applied mathematics.; Engineering mathematics.; Functions of a Complex Variable.; Approximations and Expansions.; Numerical Analysis.; Global Analysis and Analysis on Manifolds.; Numerical and Computational Physics.; Appl.Mathematics/Computational Methods of Engineering.

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 approa...

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.