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

Newton’s Method01:30

Newton’s Method

182
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.
182
Rationalizing Substitutions01:29

Rationalizing Substitutions

152
Integrals involving non-rational functions are often difficult to evaluate using standard techniques, especially when radicals appear in the integrand. Rationalizing substitution provides a systematic method for simplifying such integrals by converting them into rational forms that are easier to handle.Consider a rod whose linear mass density depends on a constant linear density, a characteristic length, and the distance from the left end of the rod. Determining the total mass requires...
152
Integration of Rational Functions Using Partial Fractions01:29

Integration of Rational Functions Using Partial Fractions

309
Rational functions are expressions written as the ratio of two polynomials, and their integrals are evaluated by simplifying the integrand into manageable parts. These functions are classified as proper or improper based on the degrees of the numerator and denominator.A rational function is proper when the degree of the numerator is less than the degree of the denominator. In this case, partial fraction decomposition is used to rewrite the function as a sum of simpler rational terms. The...
309
Derivatives01:15

Derivatives

445
DerivativesThe concept of instantaneous rate of change is fundamental in both mathematics and physics, particularly in describing how a moving object alters its position with respect to time. This rate is captured mathematically through the derivative of a function. The derivative at a point represents the slope of the tangent line to the curve of the function at that point and quantifies how the function’s output changes per infinitesimal change in input.Derivative of the Square Root...
445
Linearization and Approximation01:26

Linearization and Approximation

213
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...
213
Slant Asymptotes01:27

Slant Asymptotes

238
A function's behavior is often guided by asymptotic constraints, where one term dominates another, defining a limiting trend. In the given scenario, the mathematical pattern follows a rational function: a cubic term in the numerator is divided by a squared term in the denominator. This results in a function with distinct characteristics, including an oblique asymptote, critical points, and undefined regions.The function's validity is determined by the denominator, which must be nonzero. This...
238

You might also read

Related Articles

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

Sort by
Same author

Mathematical modeling and control of lung cancer with IL2 cytokine and anti-PD-L1 inhibitor effects for low immune individuals.

PloS one·2024
Same author

Optimal sixteenth order convergent method based on quasi-Hermite interpolation for computing roots.

TheScientificWorldJournal·2014
See all related articles

Related Experiment Video

Updated: Apr 16, 2026

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

5.1K

A general class of derivative free optimal root finding methods based on rational interpolation.

Fiza Zafar1, Nusrat Yasmin1, Saima Akram1

  • 1Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan.

Thescientificworldjournal
|February 28, 2015
PubMed
Summary

Researchers developed new derivative-free iterative methods for solving equations, achieving optimal convergence speed. These efficient methods offer a superior alternative to existing techniques, simplifying the initial steps of computation.

More Related Videos

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
09:37

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data

Published on: April 26, 2016

9.1K
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

Related Experiment Videos

Last Updated: Apr 16, 2026

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

5.1K
Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
09:37

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data

Published on: April 26, 2016

9.1K
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:

  • Numerical Analysis
  • Computational Mathematics
  • Algorithm Development

Background:

  • Iterative methods are crucial for approximating solutions to complex mathematical problems.
  • Existing methods often require derivative information or complex initial steps, limiting their applicability.
  • The pursuit of higher-order convergence and derivative-free approaches remains a key research area.

Purpose of the Study:

  • To introduce a novel general class of derivative-free iterative methods.
  • To achieve an optimal order of convergence of 2(n-1) for these new methods.
  • To develop methods that bypass the need for Newton's iterate in the initial step.

Main Methods:

  • Construction of a new class of iterative methods using rational interpolants.
  • Analysis of the order of convergence for the proposed methods.
  • Derivation of special cases from the general class.
  • Implementation of numerical computations to validate performance.

Main Results:

  • A new general class of derivative-free n-point iterative methods was successfully constructed.
  • The methods achieve an optimal order of convergence of 2(n-1).
  • The proposed schemes do not require Newton's iterate in the first step.
  • Numerical results demonstrate the efficiency of the new methods.

Conclusions:

  • The developed derivative-free iterative methods are efficient and effective.
  • These methods represent a significant improvement and offer better alternatives to existing techniques.
  • The simplification in the initial steps enhances practical usability.