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

Implicit Differentiation: Problem Solving01:29

Implicit Differentiation: Problem Solving

160
Curves defined implicitly, where variables cannot be separated algebraically, require specialized techniques for analysis. The conchoid of Nicomedes exemplifies such a case. Its equation links x and y in a way that prevents isolation of one variable, making implicit differentiation essential to determine the slope and behavior at any point on the curve.The implicit form of the conchoid can be expressed as:To differentiate this equation, y is treated as a function of x, and the chain rule is...
160
Application of Nonlinear Inequalities01:29

Application of Nonlinear Inequalities

314
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...
314
Newton’s Method01:30

Newton’s Method

166
Newton’s Method is a powerful iterative technique for approximating the roots of real-valued, differentiable functions, particularly when analytical solutions are impractical. This approach is widely used in scientific computing, engineering, and finance, where equations may be too complex for traditional algebraic methods to handle. The method relies on an iterative process that refines an initial estimate using the function’s derivative to approach the true solution progressively.
166
Quadratic Models01:23

Quadratic Models

324
Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
324
Quadratic Equations01:29

Quadratic Equations

571
A quadratic equation is an algebraic expression where a variable is raised to the second power and combined with its first power and a constant; all equated to zero. These equations are frequently used to model relationships involving area, motion, and optimization. The general representation of a quadratic equation iswhere a, b, and c are real values, and a is nonzero to ensure the presence of the squared term.One method for solving a quadratic equation involves rewriting it as a product of...
571
Second Derivatives of Implicit Functions01:29

Second Derivatives of Implicit Functions

193
Elliptical arches are fundamental in architectural and structural engineering, offering aesthetic appeal and structural efficiency. The shape of an elliptical arch follows a constrained geometric relationship where the height and horizontal position are implicitly related. This means that the height y cannot be explicitly expressed as a function of the horizontal position x, necessitating implicit differentiation for slope and curvature analysis.The equation of an ellipse centered at the origin...
193

You might also read

Related Articles

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

Sort by
Same author

Encephalomyocarditis virus impairs the blood-brain barrier by degrading tight junction proteins via AKT3-dependent autophagic and apoptotic pathways.

Virulence·2026
Same author

Decoupling Bulk Homogenization and Interfacial Reconstruction via a Triple-Alkali-Cation Interlayer for High-Performance Perovskite Solar Cells.

Advanced materials (Deerfield Beach, Fla.)·2026
Same author

Shared drone route scheduling optimization.

PloS one·2026
Same author

EMCV Non-Structural Protein 2C Antagonizes cGAS-STING-Mediated Type I Interferon Signaling via Promoting K48-Linked Polyubiquitination and Degradation of STING.

Viruses·2026
Same author

Joint Impact of Body Mass Index and High-Sensitivity C-Reactive Protein on Metabolic Dysfunction-Associated Steatotic Liver Disease Risk in Type 2 Diabetes.

Metabolic syndrome and related disorders·2026
Same author

YWHAZ downregulated innate immune responses to RNA viruses by inhibiting the IRF3 signaling pathway.

mSphere·2026
Same journal

Analysis of strength degradation of coal and rock masses and stability of mined areas under long term immersion environment.

PloS one·2026
Same journal

Biogenic Silver-Selenium nanocomposite with anticancer activity and potent efficacy against vancomycin-resistant Staphylococcus aureus.

PloS one·2026
Same journal

Preparation and physicochemical characterization of a biodegradable chitosan/carboxymethyl cellulose hydrogel synthesized in NaOH/urea medium.

PloS one·2026
Same journal

Action-guilt, survivor-guilt, and depression in combat-related PTSD.

PloS one·2026
Same journal

Explainable machine learning for predicting activities of daily living at discharge in stroke patients: A retrospective study using SHAP interpretability.

PloS one·2026
Same journal

Deep learning based two-way feature depiction model for brain tumor detection.

PloS one·2026
See all related articles

Related Experiment Video

Updated: Apr 3, 2026

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

2.2K

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained

Xiangrong Li1, Xupei Zhao2, Xiabin Duan1

  • 1Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, P.R. China.

Plos One
|September 19, 2015
PubMed
Summary
This summary is machine-generated.

A new Polak-Ribière-Polak (PRP) method with a restart strategy offers improved convergence for optimization problems. This enhanced conjugate gradient (CG) method achieves both linear and quadratic convergence, outperforming standard CG algorithms in numerical tests.

Related Experiment Videos

Last Updated: Apr 3, 2026

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

2.2K

Area of Science:

  • Optimization Theory
  • Numerical Analysis
  • Computer Science

Background:

  • The conjugate gradient (CG) method typically exhibits linear convergence due to its reliance on linear approximations.
  • Achieving quadratic convergence in optimization algorithms is challenging and often limited.

Purpose of the Study:

  • To introduce a novel Polak-Ribière-Polak (PRP) method incorporating a restart strategy.
  • To enhance convergence rates by utilizing both function and gradient information.
  • To demonstrate linear and quadratic convergence properties of the new PRP method.

Main Methods:

  • Development of a new PRP algorithm with an integrated restart strategy.
  • Inclusion of n-step quadratic convergence, function value, and gradient value information.
  • Application of Armijo line search or Wolfe line search for convergence analysis.

Main Results:

  • The proposed PRP method demonstrates both linear and quadratic convergence.
  • Numerical experiments indicate the new PRP algorithm is competitive with standard CG methods.
  • The enhanced method effectively utilizes function and gradient information for faster convergence.

Conclusions:

  • The new PRP method provides a significant improvement over traditional CG approaches.
  • The integration of restart strategies and comprehensive information utilization enhances optimization efficiency.
  • The algorithm shows promise for practical applications requiring rapid convergence in optimization problems.