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Towards Intelligent Modeling: Statistical Approximation Theory

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Feldname	Details
Vorliegende Sprache	eng
Hinweise auf parallele Ausgaben	348004400 Buchausg. u.d.T.: ‡Anastassiou, George A., 1952 - : Towards intelligent modeling: statistical approximation theory
ISBN	978-3-642-19825-0
Name	Anastassiou, George A.
Name	Duman, Oktay
Name ANZEIGE DER KETTE	Duman, Oktay
T I T E L	Towards Intelligent Modeling: Statistical Approximation Theory
Verlagsort	Berlin, Heidelberg
Verlag	Springer Berlin Heidelberg
Erscheinungsjahr	2011
Erscheinungsjahr	2011
Umfang	Online-Ressource (XVI, 236p, digital)
Reihe	Intelligent Systems Reference Library ; 14
Notiz / Fußnoten	Includes bibliographical references and index
Weiterer Inhalt	Title Page; Preface; Contents; Introduction; Background and Preliminaries; Chapters Description; Statistical Approximation by Bivariate Picard Singular Integral Operators; Definition of the Operators; Estimates for the Operators; Statistical Approximation of the Operators; Conclusions; Uniform Approximation in Statistical Sense by Bivariate Gauss-Weierstrass Singular Integral Operators; Definition of the Operators; Estimates for the Operators; Statistical Approximation of the Operators; Conclusions; Statistical L_p-Convergence of Bivariate Smooth Picard Singular Integral Operators. Definition of the OperatorsEstimates for the Operators; Statistical L_p-Approximation of the Operators; Conclusions; Statistical L_p-Approximation by Bivariate Gauss-Weierstrass Singular Integral Operators; Definition of the Operators; Estimates for the Operators; Statistical L_p-Approximation by the Operators; Conclusions; A Baskakov-Type Generalization of Statistical Approximation Theory; Statistical Korovkin-Type Theorems; Statistical Approximation to Derivatives of Functions; Weighted Approximation in Statistical Sense to Derivatives of Functions. Statistical Approximation Theorems on Weighted SpacesConclusions; Statistical Approximation to Periodic Functions by a General Family of Linear Operators; Basics; A Statistical Approximation Theorem for Periodic Case; Relaxing the Positivity Condition of Linear Operators in Statistical Korovkin Theory; Statistical Korovkin-Type Results; Conclusions; Statistical Approximation Theory for Stochastic Processes; Statistical Korovkin-Type Results for Stochastic Processes; Conclusions; Statistical Approximation Theory for Multivariate Stochastic Processes; Statistical Korovkin-Type Results. ConclusionsFractional Korovkin-Type Approximation Theory Based on Statistical Convergence; Fractional Derivatives and Positive Linear Operators; Fractional Korovkin Results Based on Statistical Convergence; Conclusions; Fractional Trigonometric Korovkin Theory Based on Statistical Convergence; Fractional Derivatives in Trigonometric Case; Fractional Trigonometric Korovkin Results in Statistical Sense; Conclusions; Statistical Fuzzy Approximation Theory by Fuzzy Positive Linear Operators; Statistical Fuzzy Korovkin Theory; Statistical Fuzzy Rates. Statistical Fuzzy Trigonometric Korovkin-Type Approximation TheoryStatistical Fuzzy Trigonometric Korovkin Theory; Statistical Fuzzy Rates in Trigonometric Case; High Order Statistical Fuzzy Korovkin-Type Approximation Theory; High Order Statistical Fuzzy Korovkin Theory; Conclusions; Statistical Approximation by Bivariate Complex Picard Integral Operators; Definition and Geometric Properties of the Operators; Statistical Approximation of the Operators; Statistical Approximation by Bivariate Complex Gauss-Weierstrass Integral Operators; Definition and Geometric Properties of the Operators. Statistical Approximation of the Operators
Titelhinweis	Buchausg. u.d.T.: ‡Anastassiou, George A., 1952 - : Towards intelligent modeling: statistical approximation theory
ISBN	ISBN 978-3-642-19826-7
Klassifikation	UYQ
	COM004000
	*41-02
	006.3
	511.4
	519.2
	Q342
Kurzbeschreibung	The 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.
1. Schlagwortkette	Approximationstheorie
1. Schlagwortkette	Korovkin-Satz
SWB-Titel-Idn	343196247
Signatur	Springer E-Book
Bemerkungen	Elektronischer Volltext - Campuslizenz
Elektronische Adresse	$uhttp://dx.doi.org/10.1007/978-3-642-19826-7
Internetseite / Link	Volltext
Siehe auch	Volltext
Siehe auch	Inhaltstext

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