By Andrei Bogatyrev,Nikolai G. Kruzhilin
The difficulties of conditional optimization of the uniform (or C-) norm for polynomials and rational services come up in a number of branches of technological know-how and expertise. Their numerical resolution is notoriously tricky in case of excessive measure features. The publication develops the classical Chebyshev's procedure which supplies analytical illustration for the answer when it comes to Riemann surfaces. The concepts born within the distant (at the 1st look) branches of arithmetic comparable to complicated research, Riemann surfaces and Teichmüller conception, foliations, braids, topology are utilized to approximation difficulties.
The key function of this e-book is the use of attractive rules of latest arithmetic for the answer of utilized difficulties and their potent numerical recognition. this is often one of many few books the place the computational facets of the better genus Riemann surfaces are illuminated. powerful paintings with the moduli areas of algebraic curves offers vast possibilities for numerical experiments in arithmetic and theoretical physics.
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Extremal Polynomials and Riemann Surfaces (Springer Monographs in Mathematics) by Andrei Bogatyrev,Nikolai G. Kruzhilin