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

Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

705
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
705
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

1.3K
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
1.3K
Statically Indeterminate Problem Solving01:16

Statically Indeterminate Problem Solving

889
Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
889
Gaussian Elimination: Problem Solving01:30

Gaussian Elimination: Problem Solving

293
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...
293
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

414
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...
414
Application of Nonlinear Inequalities01:29

Application of Nonlinear Inequalities

328
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...
328

You might also read

Related Articles

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

Sort by
Same author

Correction: Regulation of focal adhesion dynamics and cell motility by the EB2 and Hax1 protein complex.

The Journal of biological chemistry·2019
Same author

Chemical Syntheses and Chemical Biology of Carboxyl Polyether Ionophores: Recent Highlights.

Angewandte Chemie (International ed. in English)·2019
Same author

Cholesterol content in cell membrane maintains surface levels of ErbB2 and confers a therapeutic vulnerability in ErbB2-positive breast cancer.

Cell communication and signaling : CCS·2019
Same author

Exercise interventions on patients with end-stage renal disease: a systematic review.

Clinical rehabilitation·2019
Same author

Long-term creep deformations in colloidal calcium-silicate-hydrate gels by accelerated aging simulations.

Journal of colloid and interface science·2019
Same author

Microconcave MAPbBr<sub>3</sub> Single Crystal for High-Performance Photodetector.

The journal of physical chemistry letters·2019
Same journal

A DECOMPOSITION ALGORITHM FOR TWO-STAGE STOCHASTIC PROGRAMS WITH NONCONVEX RECOURSE FUNCTIONS.

SIAM journal on optimization : a publication of the Society for Industrial and Applied Mathematics·2025
Same journal

ORTHOGONAL TRACE-SUM MAXIMIZATION: TIGHTNESS OF THE SEMIDEFINITE RELAXATION AND GUARANTEE OF LOCALLY OPTIMAL SOLUTIONS.

SIAM journal on optimization : a publication of the Society for Industrial and Applied Mathematics·2023
Same journal

NOISY MATRIX COMPLETION: UNDERSTANDING STATISTICAL GUARANTEES FOR CONVEX RELAXATION VIA NONCONVEX OPTIMIZATION.

SIAM journal on optimization : a publication of the Society for Industrial and Applied Mathematics·2021
Same journal

ANOTHER LOOK AT THE FAST ITERATIVE SHRINKAGE/THRESHOLDING ALGORITHM (FISTA).

SIAM journal on optimization : a publication of the Society for Industrial and Applied Mathematics·2018
Same journal

On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces.

SIAM journal on optimization : a publication of the Society for Industrial and Applied Mathematics·2010
See all related articles

Related Experiment Video

Updated: Apr 18, 2026

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques
07:16

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques

Published on: October 20, 2023

2.1K

A STRICTLY CONTRACTIVE PEACEMAN-RACHFORD SPLITTING METHOD FOR CONVEX PROGRAMMING.

He Bingsheng1, Han Liu2, Zhaoran Wang3

  • 1International Centre of Management Science and Engineering, and Department of Mathematics, Nanjing University, Nanjing, 200093, China. This author was supported by NSFC grant 91130007 and MOEC fund 20110091110004.

SIAM Journal on Optimization : a Publication of the Society for Industrial and Applied Mathematics
|January 27, 2015
PubMed
Summary
This summary is machine-generated.

The Peaceman-Rachford splitting method (PRSM) offers faster convergence than Douglas-Rachford splitting method (DRSM) for convex minimization problems. A modified PRSM with a relaxation factor guarantees faster convergence for statistical learning and image processing applications.

Keywords:
Peaceman–Rachford splitting methodcontractionconvergence rateconvex programming

More Related Videos

Facile Protocol for the Synthesis of Self-assembling Polyamine-based Peptide Amphiphiles PPAs and Related Biomaterials
08:55

Facile Protocol for the Synthesis of Self-assembling Polyamine-based Peptide Amphiphiles PPAs and Related Biomaterials

Published on: June 25, 2018

8.6K
Author Spotlight: A Computational Approach to Decipher Amino Acid Preferences in Multispecific Protein-Protein Interactions
06:50

Author Spotlight: A Computational Approach to Decipher Amino Acid Preferences in Multispecific Protein-Protein Interactions

Published on: January 26, 2024

2.7K

Related Experiment Videos

Last Updated: Apr 18, 2026

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques
07:16

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques

Published on: October 20, 2023

2.1K
Facile Protocol for the Synthesis of Self-assembling Polyamine-based Peptide Amphiphiles PPAs and Related Biomaterials
08:55

Facile Protocol for the Synthesis of Self-assembling Polyamine-based Peptide Amphiphiles PPAs and Related Biomaterials

Published on: June 25, 2018

8.6K
Author Spotlight: A Computational Approach to Decipher Amino Acid Preferences in Multispecific Protein-Protein Interactions
06:50

Author Spotlight: A Computational Approach to Decipher Amino Acid Preferences in Multispecific Protein-Protein Interactions

Published on: January 26, 2024

2.7K

Area of Science:

  • Optimization Methods
  • Numerical Analysis

Background:

  • The Douglas-Rachford splitting method (DRSM) is a foundational algorithm in optimization.
  • The Peaceman-Rachford splitting method (PRSM) is an alternative splitting method.
  • Both methods are related to the alternating direction method of multipliers.

Purpose of the Study:

  • To analyze the convergence properties of the Peaceman-Rachford splitting method (PRSM) for convex minimization.
  • To compare PRSM with the Douglas-Rachford splitting method (DRSM).
  • To propose a modified PRSM with improved convergence guarantees.

Main Methods:

  • Analysis of iterative sequence contraction properties.
  • Establishing convergence rates in ergodic and non-ergodic senses.
  • Introducing a relaxation factor to enhance PRSM's convergence.
  • Numerical validation in statistical learning and image processing.

Main Results:

  • PRSM converges faster than DRSM when convergent, but requires stricter assumptions.
  • DRSM's iterative sequence is strictly contractive, while PRSM's is contractive to the solution set.
  • A worst-case O(1/t) ergodic convergence rate for PRSM is established under mild assumptions.
  • A strictly contractive PRSM with a relaxation factor achieves a worst-case O(1/t) non-ergodic convergence rate.

Conclusions:

  • The modified PRSM demonstrates numerical efficiency for practical applications.
  • PRSM can be enhanced to guarantee strict contraction and faster convergence.
  • The study provides theoretical convergence rates for PRSM and its variants.