000			03838nam a22004695i 4500
001			978-3-642-19826-7
003			DE-He213
005			20140220083758.0
007			cr nn 008mamaa
008			110406s2011 gw | s |||| 0|eng d
020			_a9783642198267 _9978-3-642-19826-7
024	7		_a10.1007/978-3-642-19826-7 _2doi
050		4	_aQ342
072		7	_aUYQ _2bicssc
072		7	_aCOM004000 _2bisacsh
082	0	4	_a006.3 _223
100	1		_aAnastassiou, George A. _eauthor.
245	1	0	_aTowards Intelligent Modeling: Statistical Approximation Theory _h[electronic resource] / _cby George A. Anastassiou, Oktay Duman.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2011.
300			_aXVI, 236 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aIntelligent Systems Reference Library, _x1868-4394 ; _v14
505	0		_a Introduction -- Statistical Approximation by Bivariate Picard Singular Integral Operators -- Uniform Approximation in Statistical Sense by Bivariate Gauss-Weierstrass Singular Integral Operators -- Statistical Lp-Convergence of Bivariate Smooth Picard Singular Integral Operators -- Statistical Lp-Approximation by Bivariate Gauss-Weierstrass Singular Integral Operators -- A Baskakov-Type Generalization of Statistical Approximation Theory -- Weighted Approximation in Statistical Sense to Derivatives of Functions -- Statistical Approximation to Periodic Functions by a General Family of Linear Operators -- Relaxing the Positivity Condition of Linear Operators in Statistical Korovkin Theory -- Statistical Approximation Theory for Stochastic Processes -- Statistical Approximation Theory for Multivariate Stochas tic Processes.
520			_aThe main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory, fuzzy logic theory, summability theory, and so on. In this monograph we consider this concept in approximating a function by linear operators, especially when the classical limit fails. The results of this book not only cover the classical and statistical approximation theory, but also are applied in the fuzzy logic via the fuzzy-valued operators. The authors in particular treat the important Korovkin approximation theory of positive linear operators in statistical and fuzzy sense. They also present various statistical approximation theorems for some specific real and complex-valued linear operators that are not positive. This is the first monograph in Statistical Approximation Theory and Fuzziness. The chapters are self-contained and several advanced courses can be taught. The research findings will be useful in various applications including applied and computational mathematics, stochastics, engineering, artificial intelligence, vision and machine learning. This monograph is directed to graduate students, researchers, practitioners and professors of all disciplines.
650		0	_aEngineering.
650		0	_aArtificial intelligence.
650	1	4	_aEngineering.
650	2	4	_aComputational Intelligence.
650	2	4	_aArtificial Intelligence (incl. Robotics).
650	2	4	_aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
700	1		_aDuman, Oktay. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642198250
830		0	_aIntelligent Systems Reference Library, _x1868-4394 ; _v14
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-19826-7
912			_aZDB-2-ENG
999			_c107655 _d107655