Quantitative Approximations

Quantitative Approximations

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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.show more

Product details

  • Hardback | 624 pages
  • 163.6 x 242.3 x 37.3mm | 1,094.82g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 150 black & white illustrations
  • 1584882212
  • 9781584882213

Review quote

"George Anastassiou has done a tremendous job in showing the diversity of quantitative approximation methodsI am pleased to see an enormous collection of essential quantitative resultsthere is no doubt that this book should be on the desk of any student or specialist with interests in approximation, limit theorems, and more broadly quantitative mathematical methods and their applications" -Zari Rachev, University of California, Santa Barbara "The emphasis of the results presented in this monograph is quantitative, thus, for example, all mathematical entities such as operators or constants are defined precisely. This makes the material accessible to a wide audience of graduate students and scientists. The book is well written and contains a very extensive summary of the author's work over the last fifteen years." --Steven B. Damelin, in Mathematical Reviews, Issue 2001hshow more

Table of contents

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 Inequalitiesshow more