000			03325nam a2200301za04500
001			17608
008			050703s2011 gw eng d
020			_a9783642198267 99783642198267
082			_a006.3 _b223
100			_aAnastassiou, George A. _eauthor. _935064
245			_aTowards Intelligent Modeling: _bStatistical Approximation Theory _h[electronic resource] / _cby George A. Anastassiou, Oktay Duman.
300			_aXVI, 236 p. _bonline resource.
490			_aIntelligent Systems Reference Library
490			_x-1868-4394 ; _v-14
505			_aIntroduction -- 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			_aEngineering. _996
650			_aArtificial intelligence. _933648
650			_aEngineering. _996
650			_aArtificial Intelligence (incl. Robotics). _923200
650			_933838 _aSTATICS FOR ENGINEERING, PHYSICS, COMPUTERS SCIENCE, CHEMISTRY AND EARTH SCIENCES
650			_933763 _aCOMPUTATIONAL INTELIGENCE
700			_aDuman, Oktay. _936041
700			_eauthor. _936042
710			_aSpringerLink (Online service) _9111
856			_uhttp://springer.escuelaing.metaproxy.org/book/10.1007/978-3-642-19826-7 _yir a documento _qURL
942			_2ddc _cCF
999			_c14233 _d14233