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Intelligent Mathematics: Computational Analysis

  • George A. Anastassiou

Part of the Intelligent Systems Reference Library book series (ISRL, volume 5)

Table of contents

  1. Front Matter
  2. George A. Anastassiou
    Pages 1-11
  3. George A. Anastassiou
    Pages 13-27
  4. George A. Anastassiou
    Pages 29-40
  5. George A. Anastassiou
    Pages 41-56
  6. George A. Anastassiou
    Pages 69-87
  7. George A. Anastassiou
    Pages 89-91
  8. George A. Anastassiou
    Pages 99-113
  9. George A. Anastassiou
    Pages 273-274
  10. George A. Anastassiou
    Pages 275-280
  11. George A. Anastassiou
    Pages 281-298
  12. George A. Anastassiou
    Pages 299-331
  13. George A. Anastassiou
    Pages 333-354
  14. George A. Anastassiou
    Pages 399-422
  15. George A. Anastassiou
    Pages 423-433
  16. George A. Anastassiou
    Pages 575-585
  17. George A. Anastassiou
    Pages 587-600
  18. George A. Anastassiou
    Pages 601-613
  19. George A. Anastassiou
    Pages 615-625
  20. George A. Anastassiou
    Pages 627-648
  21. George A. Anastassiou
    Pages 649-672
  22. George A. Anastassiou
    Pages 673-694
  23. George A. Anastassiou
    Pages 765-772
  24. Back Matter

About this book

Introduction

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.

Keywords

Computational Analysis Fractional Approximation Intelligent Systems Neural Networks

Authors and affiliations

  • George A. Anastassiou
    • 1
  1. 1.Department of Mathematical Sciences University of MemphisMemphisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-17098-0
  • Copyright Information Springer Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-17097-3
  • Online ISBN 978-3-642-17098-0
  • Series Print ISSN 1868-4394
  • Series Online ISSN 1868-4408
  • Buy this book on publisher's site