Intelligent Mathematics: Computational Analysis [electronic resource] / by George A. Anastassiou.

Colaborador(es): Anastassiou, George A | [author.] | SpringerLink (Online service)Tipo de material: TextoTextoSeries Intelligent Systems Reference Library; -5Descripción: XVIII, 802p. 1 illus. online resourceISBN: 9783642170980 99783642170980Tema(s): Engineering | Artificial intelligence | Engineering | Artificial Intelligence (incl. Robotics) | COMPUTATIONAL INTELIGENCEClasificación CDD: 006.3 Recursos en línea: ir a documento
Contenidos:
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.
Resumen: 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.
Etiquetas de esta biblioteca: No hay etiquetas de esta biblioteca para este título. Ingresar para agregar etiquetas.
    Valoración media: 0.0 (0 votos)
Tipo de ítem Ubicación actual Colección Signatura Info Vol Copia número Estado Fecha de vencimiento Código de barras Reserva de ítems
DOCUMENTOS DIGITALES DOCUMENTOS DIGITALES Biblioteca Jorge Álvarez Lleras
Digital 006.3 223 (Navegar estantería) Ej. 1 1 Disponible D000466
Total de reservas: 0

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.

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.

No hay comentarios en este titulo.

para colocar un comentario.