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Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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.
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State Function, Exact and Inexact Differentials01:27

State Function, Exact and Inexact Differentials

A state function is a thermodynamic property that depends solely on the current state of a system, irrespective of its history or how it arrived at that state. These functions are represented by capital letters, such as U, H, and S, which stand for internal energy, enthalpy, and entropy, respectively.For instance, the value of internal energy depends on the system's state variables and remains unaffected by the process path. This means that whether the system underwent a linear process or a...
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...
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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...

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Related Experiment Video

Updated: Jul 7, 2026

A Tactile Automated Passive-Finger Stimulator (TAPS)
19:44

A Tactile Automated Passive-Finger Stimulator (TAPS)

Published on: June 3, 2009

Stochastic choice of basis functions in adaptive function approximation and the functional-link net.

B Igelnik1, Y H Pao

  • 1Dept. of Electr. Eng. and Appl. Phys., Case Western Reserve Univ., Cleveland, OH.

IEEE Transactions on Neural Networks
|January 1, 1995
PubMed
Summary

The random vector functional-link (RVFL) net is a universal approximator for continuous functions. This adaptive network efficiently approximates functions with a convergence rate of O(C/√n), enhancing machine learning capabilities.

Related Experiment Videos

Last Updated: Jul 7, 2026

A Tactile Automated Passive-Finger Stimulator (TAPS)
19:44

A Tactile Automated Passive-Finger Stimulator (TAPS)

Published on: June 3, 2009

Area of Science:

  • Machine Learning
  • Computational Mathematics
  • Artificial Intelligence

Background:

  • Adaptive function approximation is crucial for machine learning and data analysis.
  • Existing methods often face challenges in efficiency and accuracy for complex functions.
  • The random vector functional-link (RVFL) net offers a novel approach to function approximation.

Purpose of the Study:

  • To provide a theoretical justification for the random vector version of the functional-link (RVFL) net.
  • To establish the RVFL net's capabilities as a universal approximator.
  • To analyze the efficiency and convergence rate of the RVFL net in function approximation.

Main Methods:

  • Formulating a limit-integral representation of the function to be approximated.
  • Evaluating the integral using the Monte-Carlo method for theoretical analysis.
  • Investigating neural networks with hidden nodes implemented as products of univariate functions or radial basis functions.

Main Results:

  • The RVFL net is proven to be a universal approximator for continuous functions on bounded finite-dimensional sets.
  • The RVFL net demonstrates efficient approximation with an error convergence rate of O(C/√n), where n is the number of basis functions.
  • Similar universal approximation and efficiency results are observed for neural nets using product or radial basis function hidden nodes.

Conclusions:

  • The RVFL net provides a theoretically sound and efficient method for adaptive function approximation.
  • The findings support the RVFL net's potential for various machine learning applications requiring accurate function approximation.
  • Further research can explore methods to enhance the accuracy of multivariate function approximations using RVFL nets.