Intelligent Systems Reference Library

Intelligent Mathematics: Computational Analysis

Authors: Anastassiou, George A.

  • Presents the principles of computational analysis related to intelligent systems
  • Written by a leading expert in the field
Show all benefits

Buy this book

eBook $299.00
price for USA (gross)
  • ISBN 978-3-642-17098-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $379.00
price for USA
  • ISBN 978-3-642-17097-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $379.00
price for USA
  • ISBN 978-3-642-43658-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

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.

Reviews

From the reviews:

“G. A. Anastassiou is a very prolific author. His work, which has appeared in 83 papers and books during the period 1990-2010, is restructured and completed to form the 45 chapters (plus an introductory survey) of this monograph. Each chapter is self-contained and can be read independently. … The book has the advantage of bringing together the work of the author in a systematic way, and hence it is quite useful for researchers working in this direction.” (A. Bultheel, Mathematical Reviews, January, 2013)


Table of contents (46 chapters)

  • Introduction

    Anastassiou, George A.

    Pages 1-11

  • Convex Probabilistic Wavelet Like Approximation

    Anastassiou, George A.

    Pages 13-27

  • Bidimensional Constrained Wavelet Like Approximation

    Anastassiou, George A.

    Pages 29-40

  • Multidimensional Probabilistic Scale Approximation

    Anastassiou, George A.

    Pages 41-56

  • Multidimensional Probabilistic Approximation in Wavelet Like Structure

    Anastassiou, George A.

    Pages 57-67

Buy this book

eBook $299.00
price for USA (gross)
  • ISBN 978-3-642-17098-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $379.00
price for USA
  • ISBN 978-3-642-17097-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $379.00
price for USA
  • ISBN 978-3-642-43658-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Intelligent Mathematics: Computational Analysis
Authors
Series Title
Intelligent Systems Reference Library
Series Volume
5
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer Berlin Heidelberg
eBook ISBN
978-3-642-17098-0
DOI
10.1007/978-3-642-17098-0
Hardcover ISBN
978-3-642-17097-3
Softcover ISBN
978-3-642-43658-1
Series ISSN
1868-4394
Edition Number
1
Number of Pages
XVII, 802
Topics