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Other titles in the Intelligent Systems Reference Library series:

Intelligent Systems Reference Library #5: Intelligent Mathematics: Computational Analysis

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Intelligent Systems Reference Library #5: Intelligent Mathematics: Computational Analysis Cover

 

Synopses & Reviews

Publisher Comments:

PLEASE USE THE FILE BACK COVER! Knowledge can be modelled 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 preservation property, fractional singular operators. We also deal with non-isotropic general Picard singular multivariate operators and q-Gauss-Weierstrass singular q-integral operators.We talk about quantitative approximations by shift-invariant univariate and multivariate integral operators, nonlinear neural networks approximation, convergence with rates of positive linear operators, quantitative approximation by bounded linear operators, univariate and multivariate quantitative approximation by stochastic positive linear operators on univariate and multivariate stochastic processes. We further present right fractional calculus and give quantitative fractional Korovkin theory of positive linear operators. We also give analytical inequalities, fractional Opial inequalities, fractional identities and inequalities regarding fractional integrals.We further deal with semigroup operator approximation, simultaneous Feller probabilistic approximation. We also present Fuzzy singular operator approximations.We give transfers from real to fuzzy approximation and talk about fuzzy wavelet and fuzzy neural networks approximations, fuzzy fractional calculus and fuzzy Ostrowski inequality. We talk about discrete fractional calculus, nabla discrete fractional calculus and inequalities.We study the q-inequalities, and q-fractional inequalities. We further study time scales: delta and nabla approaches, duality principle and inequalities. We introduce delta and nabla time scales fractional calculus and inequalities.We finally study convergence with rates of approximate solutions to exact solution of multivariate Dirichlet problem and multivariate heat equation, and discuss the uniqueness of solution of general evolution partial differential equation \ in multivariate time. The exposed results are expected to find applications to: applied and computational mathematics, stochastics, engineering, artificial intelligence, vision, complexity and machine learning. This monograph is suitable for graduate students and researchers.

Synopsis:

Knowledge can be modeled and computed using computational mathematical methods, then lead to real world conclusions. This book examines a wide array of topics in computational analysis.

Synopsis:

<body>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 preservation property, fractional singular operators. We also deal with non-isotropic general Picard singular multivariate operators and q-Gauss-Weierstrass singular q-integral operators. We talk about quantitative approximations by shift-invariant univariate and multivariate integral operators, nonlinear neural networks approximation, convergence with rates of positive linear operators, quantitative approximation by bounded linear operators, univariate and multivariate quantitative approximation by stochastic positive linear operators on univariate and multivariate stochastic processes. We further present right fractional calculus and give quantitative fractional Korovkin theory of positive linear operators. We also give analytical inequalities, fractional Opial inequalities, fractional identities and inequalities regarding fractional integrals. We further deal with semi group operator approximation, simultaneous Feller probabilistic approximation. We also present Fuzzy singular operator approximations. We give transfers from real to fuzzy approximation and talk about fuzzy wavelet and fuzzy neural networks approximations, fuzzy fractional calculus and fuzzy Ostrowski inequality. We talk about discrete fractional calculus, nabla discrete fractional calculus and inequalities. We study the q-inequalities, and q-fractional inequalities. We further study time scales: delta and nabla approaches, duality principle and inequalities. We introduce delta and nabla time scales fractional calculus and inequalities. We finally study convergence with rates of approximate solutions to exact solution of multivariate Dirichlet problem and multivariate heat equation, and discuss the uniqueness of solution of general evolution partial differential equation \ in multivariate time. The exposed results are expected to find applications to: applied and computational mathematics, stochastics, engineering, artificial intelligence, vision, complexity and machine learning. This monograph is suitable for graduate students and researchers.</body>

Table of Contents

Introduction.- Convex Probabilistic Wavelet like Approximation.- Bidimensional Constrained Wavelet like Approximation.- Multidimensional Probabilistic Scale Approximation.- Multidimensional probabilistic approximation in wavelet like structure.- About L-Positive Approximations: About Shape Preserving Weighted Uniform Approximation.- Jackson-Type Nonpositive Approximations for Definite Integrals.- Discrete Best L1 Approximation using the Gauges Way.- Quantitative Uniform Convergence of Smooth Picard Singular Integral Operators.- Global Smoothness and Simultaneous Approximation by Smooth Picard Singular Operators.- Convergence Results.- Approximation with Rates by Fractional Smooth Picard.- Singular Operators.- Multivariate Generalized Picard Singular Integral Operators.- Approximation by q-Gauss-Weierstrass Singular Integral Operators.- Quantitative Approximation by Univariate Shift-Invariant.- Integral Operators.

Product Details

ISBN:
9783642170973
Author:
Anastassiou, George A.
Publisher:
Springer
Subject:
Engineering - General
Subject:
Computational Analysis
Subject:
Fractional Approximation
Subject:
intelligent systems
Subject:
Neural Networks
Subject:
Computational intelligence
Subject:
Artificial Intelligence (incl. Robotics)
Subject:
Engineering-General Engineering
Subject:
Artificial Intelligence
Copyright:
Edition Description:
2011
Series:
Intelligent Systems Reference Library
Series Volume:
5
Publication Date:
20101213
Binding:
HARDCOVER
Language:
English
Pages:
820
Dimensions:
235 x 155 mm 2910 gr

Related Subjects

Computers and Internet » Artificial Intelligence » General
Computers and Internet » Computers Reference » General
Engineering » Engineering » General Engineering

Intelligent Systems Reference Library #5: Intelligent Mathematics: Computational Analysis New Hardcover
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Product details 820 pages Springer - English 9783642170973 Reviews:
"Synopsis" by , Knowledge can be modeled and computed using computational mathematical methods, then lead to real world conclusions. This book examines a wide array of topics in computational analysis.
"Synopsis" by , <body>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 preservation property, fractional singular operators. We also deal with non-isotropic general Picard singular multivariate operators and q-Gauss-Weierstrass singular q-integral operators. We talk about quantitative approximations by shift-invariant univariate and multivariate integral operators, nonlinear neural networks approximation, convergence with rates of positive linear operators, quantitative approximation by bounded linear operators, univariate and multivariate quantitative approximation by stochastic positive linear operators on univariate and multivariate stochastic processes. We further present right fractional calculus and give quantitative fractional Korovkin theory of positive linear operators. We also give analytical inequalities, fractional Opial inequalities, fractional identities and inequalities regarding fractional integrals. We further deal with semi group operator approximation, simultaneous Feller probabilistic approximation. We also present Fuzzy singular operator approximations. We give transfers from real to fuzzy approximation and talk about fuzzy wavelet and fuzzy neural networks approximations, fuzzy fractional calculus and fuzzy Ostrowski inequality. We talk about discrete fractional calculus, nabla discrete fractional calculus and inequalities. We study the q-inequalities, and q-fractional inequalities. We further study time scales: delta and nabla approaches, duality principle and inequalities. We introduce delta and nabla time scales fractional calculus and inequalities. We finally study convergence with rates of approximate solutions to exact solution of multivariate Dirichlet problem and multivariate heat equation, and discuss the uniqueness of solution of general evolution partial differential equation \ in multivariate time. The exposed results are expected to find applications to: applied and computational mathematics, stochastics, engineering, artificial intelligence, vision, complexity and machine learning. This monograph is suitable for graduate students and researchers.</body>
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