Author : George Anastassiou
Publisher : CRC Press
Page : 622 pages
File Size : 10,8 MB
Release : 2000-09-15
Category : Mathematics
ISBN : 1482285797
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 developm
Author : George A. Anastassiou
Publisher : Springer Science & Business Media
Page : 113 pages
File Size : 16,58 MB
Release : 2011-06-02
Category : Technology & Engineering
ISBN : 3642214312
This brief monograph is the first one to deal exclusively with the quantitative approximation by artificial neural networks to the identity-unit operator. Here we study with rates the approximation properties of the "right" sigmoidal and hyperbolic tangent artificial neural network positive linear operators. In particular we study the degree of approximation of these operators to the unit operator in the univariate and multivariate cases over bounded or unbounded domains. This is given via inequalities and with the use of modulus of continuity of the involved function or its higher order derivative. We examine the real and complex cases. For the convenience of the reader, the chapters of this book are written in a self-contained style. This treatise relies on author's last two years of related research work. Advanced courses and seminars can be taught out of this brief book. All necessary background and motivations are given per chapter. A related list of references is given also per chapter. The exposed results are expected to find applications in many areas of computer science and applied mathematics, such as neural networks, intelligent systems, complexity theory, learning theory, vision and approximation theory, etc. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also for all science libraries.
Author : George A. Anastassiou
Publisher : Springer
Page : 355 pages
File Size : 45,59 MB
Release : 2018-12-07
Category : Technology & Engineering
ISBN : 3030042871
Ordinary and fractional approximations by non-additive integrals, especially by integral approximators of Choquet, Silkret and Sugeno types, are a new trend in approximation theory. These integrals are only subadditive and only the first two are positive linear, and they produce very fast and flexible approximations based on limited data. The author presents both the univariate and multivariate cases. The involved set functions are much weaker forms of the Lebesgue measure and they were conceived to fulfill the needs of economic theory and other applied sciences. The approaches presented here are original, and all chapters are self-contained and can be read independently. Moreover, the book’s findings are sure to find application in many areas of pure and applied mathematics, especially in approximation theory, numerical analysis and mathematical economics (both ordinary and fractional). Accordingly, it offers a unique resource for researchers, graduate students, and for coursework in the above-mentioned fields, and belongs in all science and engineering libraries.
Author : George A. Anastassiou
Publisher : Springer
Page : 712 pages
File Size : 18,82 MB
Release : 2015-06-23
Category : Technology & Engineering
ISBN : 3319205056
This monograph is the continuation and completion of the monograph, “Intelligent Systems: Approximation by Artificial Neural Networks” written by the same author and published 2011 by Springer. The book you hold in hand presents the complete recent and original work of the author in approximation by neural networks. Chapters are written in a self-contained style and can be read independently. Advanced courses and seminars can be taught out of this brief book. All necessary background and motivations are given per chapter. A related list of references is given also per chapter. The book’s results are expected to find applications in many areas of applied mathematics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also for all science and engineering libraries.
Author : Ronald A. Devore
Publisher : Academic Press
Page : 337 pages
File Size : 32,93 MB
Release : 2014-05-10
Category : Mathematics
ISBN : 1483265129
Quantitative Approximation provides information pertinent to nonlinear approximation, including rational approximation and optimal knot spline approximation. This book discusses spline approximation with the most emphasis on multivariate and knot independent questions. Organized into 26 chapters, this book begins with an overview of the inequality for the sharp function in terms of the maximal rearrangement. This text then examines the best co-approximation in a Hilbert space wherein the existence ad uniqueness sets are the closed flats. Other chapters consider the inverse of the coefficient matrix for the system satisfied by the B-spline coefficients of the cubic spline interpolant at knots. This book discusses as well the relationship between the structural properties of a function and its degree of approximation by rational functions. The final chapter deals with the problem of existence of continuous selections for metric projections and provides a solution for this problem. This book is a valuable resource for mathematicians.
Author : George A. Anastassiou
Publisher : Springer
Page : 231 pages
File Size : 22,60 MB
Release : 2017-01-13
Category : Technology & Engineering
ISBN : 331951475X
This compact book focuses on self-adjoint operators’ well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading. The book’s results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. As such, the book offers a valuable resource for researchers and graduate students alike, as well as a key addition to all science and engineering libraries.
Author : Saskia Hin
Publisher : Cambridge University Press
Page : 421 pages
File Size : 24,38 MB
Release : 2013-02-14
Category : History
ISBN : 1107310717
This book provides a fresh perspective on the population history of Italy during the late Republic. It employs a range of sources and a multidisciplinary approach to investigate demographic trends and the demographic behaviour of Roman citizens. Dr Hin shows how they adapted to changing economic, climatic and social conditions in a period of intense conquest. Her critical evaluation of the evidence on the demographic toll taken by warfare and rising societal complexity leads her to a revisionist 'middle count' scenario of population development in Italy. In tracing the population history of an ancient conquest society, she provides an accessible pathway into Roman demography which focuses on the three main demographic parameters - mortality, fertility and migration. She unites literary and epigraphic sources with demographic theory, archaeological surveys, climatic and skeletal evidence, models and comparative data. Tables, figures and maps enable readers to visualise the quantitative dynamics at work.
Author : George A. Anastassiou
Publisher : Springer Nature
Page : 501 pages
File Size : 44,60 MB
Release : 2020-11-25
Category : Technology & Engineering
ISBN : 3030569624
This book applies generalized fractional differentiation techniques of Caputo, Canavati and Conformable types to a great variety of integral inequalities e.g. of Ostrowski and Opial types, etc. Some of these are extended to Banach space valued functions. These inequalities have also great impact in numerical analysis, stochastics and fractional differential equations. The book continues with generalized fractional approximations by positive sublinear operators which derive from the presented Korovkin type inequalities and also includes abstract cases. It presents also multivariate complex Korovkin quantitative approximation theory. It follows M-fractional integral inequalities of Ostrowski and Polya types. The results are weighted so they provide a great variety of cases and applications. The second part of the book deals with the quantitative fractional Korovkin type approximation of stochastic processes and lays there the foundations of stochastic fractional calculus. The book considers both Caputo and Conformable fractional directions and derives regular and trigonometric results. The positive linear operators can be expectation operator commutative or not. This book results are expected to find applications in many areas of pure and applied mathematics and stochastics. As such this monograph is suitable for researchers, graduate students, and seminars of the above disciplines, also to be in all science and engineering libraries.
Author : Kofi Kissi Dompere
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 17,84 MB
Release : 2014-03-15
Category : Technology & Engineering
ISBN : 3319053299
This volume presents an analysis of the problems and solutions of the market mockery of the democratic collective decision-choice system with imperfect information structure composed of defective and deceptive structures using methods of fuzzy rationality. The book is devoted to the political economy of rent-seeking, rent-protection and rent-harvesting to enhance profits under democratic collective decision-choice systems. The toolbox used in the monograph consists of methods of fuzzy decision, approximate reasoning, negotiation games and fuzzy mathematics. The monograph further discusses the rent-seeking phenomenon in the Schumpeterian and Marxian political economies where the rent-seeking activities transform the qualitative character of the general capitalism into oligarchic socialism and making the democratic collective decision-choice system as an ideology rather than social calculus for resolving conflicts in preferences in the collective decision-choice space without violence.
Author : George A. Anastassiou
Publisher : Springer Nature
Page : 854 pages
File Size : 37,60 MB
Release : 2023-09-29
Category : Technology & Engineering
ISBN : 3031430212
In this book, we introduce the parametrized, deformed and general activation function of neural networks. The parametrized activation function kills much less neurons than the original one. The asymmetry of the brain is best expressed by deformed activation functions. Along with a great variety of activation functions, general activation functions are also engaged. Thus, in this book, all presented is original work by the author given at a very general level to cover a maximum number of different kinds of neural networks: giving ordinary, fractional, fuzzy and stochastic approximations. It presents here univariate, fractional and multivariate approximations. Iterated sequential multi-layer approximations are also studied. The functions under approximation and neural networks are Banach space valued.
