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008			100301s2008 gw | s |||| 0|eng d
020			_a9783540683490
024	7		_a10.1007/978-3-540-68349-0 _2doi
035			_a978-3-540-68349-0
072		7	_aPBKF _2bicssc
072		7	_aMAT034000 _2bisacsh
072		7	_aMAT037000 _2bisacsh
082	0	4	_a515.5
090			_amg
100	1		_aMastroianni, Giuseppe _99226
245	1	0	_aInterpolation Processes _h[electronic resource]: _bBasic Theory and Applications/ _cby Giuseppe Mastroianni, Gradimir V. Milovanovic.
260			_aBerlin, Heidelberg: _bSpringer Berlin Heidelberg, _c2008.
300			_aXIV, 444 p. _bdigital.
490	0		_aSpringer Monographs in Mathematics, _x1439-7382
505	0		_a1. Constructive Elements and Approaches in Approximation Theory -- 1.1 Introduction to Approximation Theory -- 1.2 Basic Facts on Trigonometric Approximation -- 1.3 Chebyshev Systems and Interpolation -- 1.4 Interpolation by Algebraic Polynomials -- 2. Orthogonal Polynomials and Weighted Polynomial Approximation -- 2.1 Orthogonal Systems and Polynomials -- 2.2 Orthogonal Polynomials on the Real Line -- 2.3 Classical Orthogonal Polynomials -- 2.4 Nonclassical Orthogonal Polynomials -- 2.5 Weighted Polynomial Approximation -- 3. Trigonometric Approximation -- 3.1 Approximating Properties of Operators -- 3.2 Discrete Operators -- 4. Algebraic Interpolation in Uniform Norm -- 4.1 Introduction and Preliminaries -- 4.2 Optimal Systems of Nodes -- 4.3 Weighted Interpolation -- 5. Applications -- 5.1 Quadrature Formulae -- 5.2 Integral Equations -- 5.3 Moment-Preserving Approximation -- 5.4 Summation of Slowly Convergent Series -- References -- Index .
520			_aThe classical books on interpolation address numerous negative results, i.e., results on divergent interpolation processes, usually constructed over some equidistant systems of nodes. The authors present, with complete proofs, recent results on convergent interpolation processes, for trigonometric and algebraic polynomials of one real variable, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. In this special, but fundamental and important field of real analysis the authors present the state of art. Some 500 references are cited, including many new results of the authors. Basic tools in this field (orthogonal polynomials, moduli of smoothness, K-functionals, etc.) as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. Beside the basic properties of the classical orthogonal polynomials the book provides new results on nonclassical orthogonal polynomials including methods for their numerical construction .
650		0	_aMathematics _943458
650		0	_aFourier analysis _937926
650		0	_aIntegral equations. _943725
650		0	_aSequences (Mathematics) _937180
650		0	_aFunctions, Special. _937966
697			_aMatemáticas Gerais- _x(inclusive alguns textos elementares sobre assuntos específicos) _923752
700	1		_aMilovanovic, Gradimir V _99227
710	1		_aSpringerLink (Online service). _98857
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540683469
830		0	_aSpringer monographs in mathematics, _924417
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-540-68349-0
942			_2impa _cEBK
999			_aMASTROIANNI, Giuseppe; MILOVANOVIC, Gradimir V. <b> Interpolation Processes: </b> Basic Theory and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. XIV, 444 p (Springer Monographs in Mathematics, 1439-7382). ISBN 9783540683490. Disponível em: <http://dx.doi.org/10.1007/978-3-540-68349-0 > _c38562 _d38562