000 05120nam a22004455i 4500
001 978-3-642-17098-0
003 DE-He213
005 20140220083750.0
007 cr nn 008mamaa
008 110318s2011 gw | s |||| 0|eng d
020 _a9783642170980
_9978-3-642-17098-0
024 7 _a10.1007/978-3-642-17098-0
_2doi
050 4 _aQ342
072 7 _aUYQ
_2bicssc
072 7 _aCOM004000
_2bisacsh
082 0 4 _a006.3
_223
100 1 _aAnastassiou, George A.
_eauthor.
245 1 0 _aIntelligent Mathematics: Computational Analysis
_h[electronic resource] /
_cby George A. Anastassiou.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2011.
300 _aXVIII, 802p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aIntelligent Systems Reference Library,
_x1868-4394 ;
_v5
505 0 _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 \ 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.
650 0 _aEngineering.
650 0 _aArtificial intelligence.
650 1 4 _aEngineering.
650 2 4 _aComputational Intelligence.
650 2 4 _aArtificial Intelligence (incl. Robotics).
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642170973
830 0 _aIntelligent Systems Reference Library,
_x1868-4394 ;
_v5
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-17098-0
912 _aZDB-2-ENG
999 _c107223
_d107223