000			04597nam a2200277za04500
001			17518
008			050703s2011 gw eng d
020			_a9783642170980 99783642170980
082			_a006.3 _b223
245			_aIntelligent Mathematics: _bComputational Analysis _h[electronic resource] / _cby George A. Anastassiou.
300			_aXVIII, 802p. 1 illus. _bonline resource.
490			_aIntelligent Systems Reference Library
490			_x-1868-4394 ; _v-5
505			_aIntroduction -- 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.
520			_aPLEASE 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 _ain 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.
650			_aEngineering. _996
650			_aArtificial intelligence. _933648
650			_aEngineering. _996
650			_aArtificial Intelligence (incl. Robotics). _923200
650			_933763 _aCOMPUTATIONAL INTELIGENCE
700			_aAnastassiou, George A. _935064
700			_eauthor. _935065
710			_aSpringerLink (Online service) _9111
856			_uhttp://springer.escuelaing.metaproxy.org/book/10.1007/978-3-642-17098-0 _yir a documento _qURL
942			_2ddc _cCF
999			_c14143 _d14143