Download Extremal Polynomials and Riemann Surfaces (Springer by Andrei Bogatyrev,Nikolai G. Kruzhilin PDF

By Andrei Bogatyrev,Nikolai G. Kruzhilin

The difficulties of conditional optimization of the uniform (or C-) norm for polynomials and rational features come up in a number of branches of technology and know-how. Their numerical resolution is notoriously tough in case of excessive measure capabilities. The e-book develops the classical Chebyshev's technique which supplies analytical illustration for the answer by way of Riemann surfaces. The concepts born within the distant (at the 1st look) branches of arithmetic similar to complicated research, Riemann surfaces and Teichmüller conception, foliations, braids, topology are utilized to  approximation difficulties.  

The key characteristic of this booklet is using appealing principles of latest arithmetic for the answer of utilized difficulties and their potent numerical cognizance. this can be one of many few books  the place the computational facets of the better genus Riemann surfaces are illuminated. potent paintings with the moduli areas of algebraic curves presents broad possibilities for numerical experiments in arithmetic and theoretical physics.​

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