Quantitative Approximations - Rilegato

Anastassiou, George

Rilegato

ISBN 10: 1584882212 ISBN 13: 9781584882213

Casa editrice: Chapman and Hall/CRC, 2000

Riassunto

Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approximations provides a thorough account of all of the significant developments in the area of contemporary quantitative mathematics. It offers readers the unique opportunity of approaching the field under the guidance of an expert.

Among the book's outstanding features is the inclusion of the introductory chapter that summarizes the primary and most useful results. This section serves not only as a more detailed table of contents for those new to an area of application, but also as a quick reference for more seasoned researchers.

The author describes all of the pertinent mathematical entities precisely and concretely. His approach and proofs are straightforward and constructive, making Quantitative Approximations accessible and valuable to researchers and graduate students alike.

Su questo libro

Contenuti:

INTRODUCTION
Summary of Results
ON NEURAL NETWORKS
Convergence with Rates of Univariate Neural Network Operators to the Unit Operator
Convergence with Rates of Multivariate Neural Network Operators to the Unit Operator
Asymptotic Weak Convergence of Cardaliaguet-Euvrard Neural Network Operators
Asymptotic Weak Convergence of Squashing Neural Network Operators
ON WAVELETS
Quantitative Monotone and Probabilistic Wavelet Type Approximation
Quantitative Multidimensional High Order Wavelet Type Approximation
More on Shape and Probability Preserving One-Dimensional Wavelet Type Operators
Quantitative Multidimensional High Order Wavelet Type Approximation
Rate of Convergence of Probabilistic Discrete Wavelet Approximation
Asymptotic Non-Orthogonal Wavelet Approximation for Deterministic Signals
Wavelet Type Differentiated Shift-Invariant Integral Operators
ON PARTIAL DIFFERENTIAL EQUATIONS
A Discrete Kac's Formula and Optimal Quantitative Approximation in the Solution of Heat Equation
ON SEMIGROUPS
Quantitative Asymptotic Expansions of the Probabilistic Representation Formulae for (C0 ) m-Parameter Operator Semigroups
ON STOCHASTICS
Quantitative Probability Limit Theorems over Banach Spaces
Quantitative Study of Bias Convergence for Generalized L-Statistics
ON FUNCTIONAL ANALYSIS
Quantitative Korovkin-Type Results for Vector Valued Functions
Quantitative Lp Results for Positive Linear Operators
ON APPROXIMATION THEORY
On Monotone Approximation Theory
Comparisons for Local Moduli of Continuity
Convergence with Rate of Univariate Singular Integrals to the Unit
ON CLASSICAL ANALYSIS
About Univariate Ostrowski Type Inequalities
About Multidimensional Ostrowski Type Inequalities
General Opial Type Inequalities for Linear Differential Operators
Lp Opial Type Inequalities Engaging Fractional Derivatives of Functions
Lp General Fractional Opial Inequalities

Su questa edizione

• Editore: Chapman and Hall/CRC
• Data di pubblicazione: 2000
• ISBN 10: 1584882212
• ISBN 13: 9781584882213
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 624