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Related Concept Videos

Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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Approximate Integration

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Multi-input and Multi-variable systems

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Related Experiment Videos

Multivariate sigmoidal neural network approximation.

George A Anastassiou1

  • 1Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA. ganastss@memphis.edu

Neural Networks : the Official Journal of the International Neural Network Society
|February 12, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces novel sigmoidal neural network operators for approximating continuous functions. These operators provide accurate pointwise and uniform approximations, enhancing function approximation capabilities.

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Area of Science:

  • Numerical Analysis
  • Machine Learning
  • Approximation Theory

Background:

  • Multivariate function approximation is crucial in various scientific fields.
  • Neural network operators offer a powerful tool for complex function approximation.
  • Existing methods may have limitations in terms of accuracy and scope.

Purpose of the Study:

  • To develop and analyze multivariate quasi-interpolation sigmoidal neural network operators.
  • To establish theoretical guarantees for the approximation accuracy.
  • To define precise operators for approximating continuous functions on boxes and RN.

Main Methods:

  • Utilizing multivariate quasi-interpolation sigmoidal neural network operators.
  • Establishing multidimensional Jackson type inequalities.
  • Employing the multivariate modulus of continuity and high-order partial derivatives.
  • Defining operators using a multidimensional density function induced by the logarithmic sigmoidal function.

Main Results:

  • The study precisely describes the effective sigmoidal neural network operators.
  • Multidimensional Jackson type inequalities are established, providing error bounds.
  • Pointwise and uniform approximation capabilities are demonstrated.
  • The feed-forward neural network architecture with one hidden layer is specified.

Conclusions:

  • The developed sigmoidal neural network operators are effective for multivariate function approximation.
  • The theoretical framework provides rigorous justification for the approximation quality.
  • This work contributes to the advancement of neural network-based approximation theory.