000			03187nam a22005295i 4500
001			978-3-642-25634-9
003			DE-He213
005			20140220083306.0
007			cr nn 008mamaa
008			120530s2012 gw | s |||| 0|eng d
020			_a9783642256349 _9978-3-642-25634-9
024	7		_a10.1007/978-3-642-25634-9 _2doi
050		4	_aQA331-355
072		7	_aPBKD _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.9 _223
100	1		_aBogatyrev, Andrei. _eauthor.
245	1	0	_aExtremal Polynomials and Riemann Surfaces _h[electronic resource] / _cby Andrei Bogatyrev.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2012.
300			_aXXV, 150 p. 47 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringer Monographs in Mathematics, _x1439-7382
505	0		_a1 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.
520			_aThe 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.
650		0	_aMathematics.
650		0	_aFunctions of complex variables.
650		0	_aGlobal analysis.
650		0	_aNumerical analysis.
650		0	_aEngineering mathematics.
650	1	4	_aMathematics.
650	2	4	_aFunctions of a Complex Variable.
650	2	4	_aApproximations and Expansions.
650	2	4	_aNumerical Analysis.
650	2	4	_aGlobal Analysis and Analysis on Manifolds.
650	2	4	_aNumerical and Computational Physics.
650	2	4	_aAppl.Mathematics/Computational Methods of Engineering.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642256332
830		0	_aSpringer Monographs in Mathematics, _x1439-7382
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-25634-9
912			_aZDB-2-SMA
999			_c102454 _d102454