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

254
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....
254
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

212
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,...
212
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

2.4K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
2.4K
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

961
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
961
Fast Decoupled and DC Powerflow01:24

Fast Decoupled and DC Powerflow

442
The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
442
Application of Nonlinear Inequalities01:29

Application of Nonlinear Inequalities

78
A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality:  can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the...
78

You might also read

Related Articles

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

Sort by
Same author

A two-term hybrid method with restart strategy for signal processing and image recovery.

Scientific reports·2026
Same author

A novel decision analytic model for environmental sustainability challenges using interval-valued complex spherical fuzzy soft sets.

Scientific reports·2026
Same author

Spectral-like conjugate gradient methods with sufficient descent property for vector optimization.

PloS one·2024
Same author

The proportional Caputo operator approach to the thermal transport of Jeffery tri-hybrid nanofluid in a rotating frame with thermal radiation.

Scientific reports·2023
Same author

Gyrotactic microorganism hybrid nanofluid over a Riga plate subject to activation energy and heat source: numerical approach.

Scientific reports·2023
Same author

Analysis of the Time-Dependent magnetohydrodynamic Newtonian fluid flow over a rotating sphere with thermal radiation and chemical reaction.

Heliyon·2023

Related Experiment Video

Updated: Nov 26, 2025

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects
10:16

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects

Published on: February 8, 2014

12.5K

Derivative-free HS-DY-type method for solving nonlinear equations and image restoration.

Auwal Bala Abubakar1,2,3, Poom Kumam1,4, Abdulkarim Hassan Ibrahim1

  • 1Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.

Heliyon
|December 9, 2020
PubMed
Summary

A new derivative-free conjugate gradient algorithm combines Hestenes-Stiefel and Dai-Yuan methods for nonlinear equations and image restoration, demonstrating efficient convergence and practical application.

Keywords:
Conjugate gradientImage restorationMathematicsNonlinear equationsProjection method

More Related Videos

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

2.0K
Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

9.8K

Related Experiment Videos

Last Updated: Nov 26, 2025

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects
10:16

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects

Published on: February 8, 2014

12.5K
Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

2.0K
Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

9.8K

Area of Science:

  • Numerical Analysis
  • Optimization
  • Image Processing

Background:

  • Nonlinear equations and image restoration are critical computational problems.
  • Derivative-free methods are desirable when gradients are unavailable or costly.
  • Conjugate gradient (CG) methods offer efficient iterative solutions for large-scale problems.

Purpose of the Study:

  • To propose a novel derivative-free conjugate gradient algorithm.
  • To enhance the performance of CG methods by hybridizing Hestenes-Stiefel (HS) and Dai-Yuan (DY) parameters.
  • To demonstrate the algorithm's efficacy in solving nonlinear equations and image restoration tasks.

Main Methods:

  • Developed a hybrid CG algorithm using a convex combination of HS and DY parameters.
  • Ensured the search direction is both descent and bounded for stability.
  • Theoretically analyzed the algorithm's convergence under standard assumptions.

Main Results:

  • The proposed hybrid algorithm exhibits descent and bounded search directions.
  • Theoretical convergence is established for the algorithm.
  • Empirical results on benchmark problems show superior efficiency compared to existing methods.
  • Successful application to image restoration problems was demonstrated.

Conclusions:

  • The proposed derivative-free hybrid CG algorithm is effective for nonlinear equations and image restoration.
  • The combination of HS and DY parameters contributes to improved performance and convergence.
  • The algorithm offers a promising alternative for practical optimization and image processing tasks.