Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
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...
Approximate Integration01:24

Approximate Integration

In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Optimizing decision making with Fermatean fuzzy soft Hamachar operators in the analysis of anaphylaxis (a life-threatening allergic reaction).

Scientific reports·2026
Same author

Finite-Time Consensus of Stochastic Delayed Multiagent Systems Subject to Lévy Noise, Markov Switching, and Actuator Fault Uncertainties.

IEEE transactions on cybernetics·2025
Same author

Significance of supervision sampling in control of communicable respiratory disease simulated by a new model during different stages of the disease.

Scientific reports·2025
Same author

Integrated explainable machine learning and multi-omics analysis for survival prediction in cancer with immunotherapy response.

Apoptosis : an international journal on programmed cell death·2024
Same author

A Boundary-Enhanced Decouple Fusion Segmentation Network for Diagnosis of Adenomatous Polyps.

Journal of imaging informatics in medicine·2024
Same author

Lightweight Attentive Graph Neural Network with Conditional Random Field for Diagnosis of Anterior Cruciate Ligament Tear.

Journal of imaging informatics in medicine·2024
Same journal

Universal perceptron and DNA-like learning algorithm for binary neural networks: LSBF and PBF implementations.

IEEE transactions on neural networks·2013
Same journal

Guest editorial: special section on white box nonlinear prediction models.

IEEE transactions on neural networks·2011
Same journal

Data-based fault-tolerant control of high-speed trains with traction/braking notch nonlinearities and actuator failures.

IEEE transactions on neural networks·2011
Same journal

Guest editorial: special section on data-based control, modeling, and optimization.

IEEE transactions on neural networks·2011
Same journal

Neural network-based multiple robot simultaneous localization and mapping.

IEEE transactions on neural networks·2011
Same journal

Data-driven model-free adaptive control for a class of MIMO nonlinear discrete-time systems.

IEEE transactions on neural networks·2011
See all related articles

Related Experiment Videos

Constructive approximation to multivariate function by decay RBF neural network.

Muzhou Hou1, Xuli Han

  • 1Central South University, Changsha, China. houmuzhou@sina.com

IEEE Transactions on Neural Networks
|August 10, 2010
PubMed
Summary
This summary is machine-generated.

This study proves decay radial basis function (RBF) neural networks can approximate functions without training. These networks offer faster convergence and better generalization than traditional methods.

Related Experiment Videos

Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Neural Networks

Background:

  • Single hidden layer feedforward networks with radial basis function (RBF) kernels are known universal approximators.
  • However, training all network parameters can lead to complex learning, poor generalization, overtraining, and instability.

Purpose of the Study:

  • To provide a constructive proof for the approximation capabilities of decay RBF neural networks.
  • To demonstrate that decay RBFs can uniformly approximate continuous multivariate functions without training.
  • To compare the performance of decay RBF networks against conventional RBF, BP, extreme learning machine, and support vector machines.

Main Methods:

  • Constructive proof of interpolation for decay RBF neural networks.
  • Theoretical analysis of uniform approximation for continuous multivariate functions using decay RBFs.
  • Numerical experiments to evaluate convergence and generalization performance.

Main Results:

  • A decay RBF neural network with n+1 hidden neurons can interpolate n+1 multivariate samples with zero error.
  • Decay RBFs can uniformly approximate any continuous multivariate function with arbitrary precision without requiring training.
  • Numerical experiments showed faster convergence and better generalization compared to conventional RBF, BP, extreme learning machine, and support vector machines.

Conclusions:

  • Decay RBF neural networks offer a viable alternative to conventional training methods.
  • The proposed approach achieves high accuracy and robust generalization without complex parameter tuning.
  • This work advances the understanding and application of RBF networks in function approximation.