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

Application of Nonlinear Inequalities01:29

Application of Nonlinear Inequalities

170
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...
170
Gaussian Elimination: Problem Solving01:30

Gaussian Elimination: Problem Solving

122
Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
122
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

234
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...
234
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

281
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,...
281
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

313
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....
313
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

18.6K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
18.6K

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: Dec 26, 2025

Lensless Fluorescent Microscopy on a Chip
11:23

Lensless Fluorescent Microscopy on a Chip

Published on: August 17, 2011

18.0K

A hybrid conjugate gradient algorithm for constrained monotone equations with application in compressive sensing.

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

  • 1KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand.

Heliyon
|March 11, 2020
PubMed
Summary

A novel hybrid conjugate gradient algorithm efficiently solves nonlinear monotone equations and restores sparse signals/images in compressive sensing. This method proves more computationally efficient and robust than existing algorithms.

Keywords:
Applied mathematicsCompressive sensingComputer scienceConjugate gradient methodConvex constraintsProjection method

More Related Videos

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

12.6K
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

Related Experiment Videos

Last Updated: Dec 26, 2025

Lensless Fluorescent Microscopy on a Chip
11:23

Lensless Fluorescent Microscopy on a Chip

Published on: August 17, 2011

18.0K
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

12.6K
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

Area of Science:

  • Numerical Analysis
  • Optimization Theory
  • Signal Processing

Background:

  • Unconstrained minimization problems are fundamental in applied mathematics.
  • Convex constrained nonlinear monotone equations arise in various scientific and engineering fields.
  • Sparse signal and image reconstruction are crucial in compressive sensing.

Purpose of the Study:

  • To propose a novel hybrid conjugate gradient algorithm.
  • To extend the algorithm for solving convex constrained nonlinear monotone equations.
  • To apply the algorithm for sparse signal and image restoration in compressive sensing.

Main Methods:

  • The proposed method combines the Solodov and Svaiter projection method with the Djordjević Liu-Storey and Fletcher Reeves conjugate gradient algorithm.
  • Global convergence is established under specific conditions.
  • The algorithm is applied to -norm regularized problems.

Main Results:

  • The hybrid conjugate gradient algorithm is successfully extended to solve convex constrained nonlinear monotone equations.
  • The method demonstrates global convergence.
  • Numerical experiments confirm the algorithm's effectiveness in sparse signal and image reconstruction.

Conclusions:

  • The proposed hybrid conjugate gradient algorithm offers an efficient and robust approach for solving nonlinear monotone equations.
  • It shows significant advantages in compressive sensing applications like sparse signal and image restoration compared to existing methods.