Knowledge can be modeled and computed using computational mathematical methods, then lead to real world conclusions. The strongly related to that Computational Analysis is a very large area with lots of applications. This monograph includes a great variety of topics of Computational Analysis. We present: probabilistic wavelet approximations, constrained abstract approximation theory, shape preserving weighted approximation, non positive approximations to definite integrals, discrete best approximation, approximation theory of general Picard singular operators including global smoothness...
Knowledge can be modeled and computed using computational mathematical methods, then lead to real world conclusions. The strongly related to that C...
Proceedings of the Conference on title], held in Santa Barbara, California, May 1993. The main topics are: approximation of functions by polynomials, splines, and operators, and applications to stochastics; numerical methods for approximation of deterministic and stochastic integrals; orthogonal po
Proceedings of the Conference on title], held in Santa Barbara, California, May 1993. The main topics are: approximation of functions by polynomials,...
Inequalities based on Sobolev Representations deals exclusively with very general tight integral inequalities of Chebyshev-Gruss, Ostrowski types and of integral means, all of which depend upon the Sobolev integral representations of functions. Applications illustrate inequalities that engage in ordinary and weak partial derivatives of the involved functions. This book also derives important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations. The results are examined in all directions and through both univariate and multivariate cases....
Inequalities based on Sobolev Representations deals exclusively with very general tight integral inequalities of Chebyshev-Gruss, Ostrowski ...
Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation....
Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals t...
This brief monograph is the first to deal exclusively with the quantitative approximation by artificial neural networks to the identity-unit operator. Each chapter is written in a self-contained style, with all necessary background and motivations included.
This brief monograph is the first to deal exclusively with the quantitative approximation by artificial neural networks to the identity-unit operat...
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...
This brief monograph is the first one to deal exclusively with the quantitative approximation by artificial neural networks to the identity-unit opera...
We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val- ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of...
We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of the...
George A. Anastassiou Svetlozar T. Rachev George A
These proceedings contain selected papers presented at the Conference on Approximation, Probability and Related Fields held in Santa Barbara, California, on May 20-22, 1993. The main topics of the conference were: 1) approximation of functions by polynomials, splines, and operators, and applications to stochastics 2) numerical methods for approximation of deterministic and stochastic integrals 3) orthogonal polynomials and stochastic processes 4) positive linear operators and related deterministic and stochastic inequalities 5) multivariate approximation and interpolation 6) rate of...
These proceedings contain selected papers presented at the Conference on Approximation, Probability and Related Fields held in Santa Barbara, Californ...
This is the first numerical analysis text to use Sage for the implementation of algorithms and can be used in a one-semester course for undergraduates in mathematics, math education, computer science/information technology, engineering, and physical sciences. The primary aim of this text is to simplify understanding of the theories and ideas from a numerical analysis/numerical methods course via a modern programming language like Sage. Aside from the presentation of fundamental theoretical notions of numerical analysis throughout the text, each chapter concludes with several exercises that...
This is the first numerical analysis text to use Sage for the implementation of algorithms and can be used in a one-semester course for undergradua...
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.
This monograph is the continuation and completion of the monograph, "Intelligent Systems: Approximation by Artificial Neural Networks" written by the ...
