A link between the steepest descent method and fixed-point iterations.

Optim Lett

Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG UK.

Published: March 2022

We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler-Lagrange equation. In this context, we shall rediscover the preconditioned algebraic conjugate gradient method for the discretised problem. The benefit of the connection of those concepts will be illustrated by a numerical experiment.

Download full-text PDF

Source
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC9813030PMC
http://dx.doi.org/10.1007/s11590-022-01867-9DOI Listing

Publication Analysis

Top Keywords

link steepest
8
steepest descent
8
descent method
8
fixed-point iterations
8
method fixed-point
4
iterations will
4
will link
4
method unconstrained
4
unconstrained minimisation
4
minimisation problem
4

Similar Publications

To develop a clinical imaging method for monitoring macrophage migration to the defect site after implantation of various stem cells and evaluating immune responses in the context of knee arthritis, T2 mapping was correlated with CD68-positive cell densities in defects and the bone marrow. This study, which was approved by the Institutional Animal Care and Use Committee, used 32 New Zealand white rabbits preloaded with ultrasmall superparamagnetic iron oxide particles (USPIOs). They were divided into groups that received different stem cell implants after osteochondral defect induction.

View Article and Find Full Text PDF
Article Synopsis
  • - The study investigates how socioeconomic status (SES) affects body mass index (BMI) trends in India over several years, using data from National Family Health Surveys between 1998 and 2021.
  • - Findings show that people in low SES groups are more likely to be underweight, while those in high SES groups tend to be overweight or obese, though the gap in these BMI categories has decreased over time.
  • - The research highlights ongoing inequalities in BMI related to SES and suggests the need for future studies to understand the factors linking these two issues.
View Article and Find Full Text PDF

Income is not an equalizer: health development inequities by ethnoracial backgrounds in California kindergartners.

BMC Public Health

December 2023

Department of Pediatrics, David Geffen School of Medicine, University of California, Los Angeles (UCLA), Center for Healthier Children, Families, and Communities, Los Angeles, USA.

Background: Early childhood health development is positively associated with income, but the strength of this relationship with ethnoracial background remains unclear. This study examined the extent of health development inequities among California kindergarteners based on ethnoracial backgrounds and neighborhood-level income.

Methods: This cross-sectional study assessed health development inequities by analyzing neighborhood-level income, ethnoracial background, and health development data for California kindergarteners.

View Article and Find Full Text PDF

A link between the steepest descent method and fixed-point iterations.

Optim Lett

March 2022

Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG UK.

We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler-Lagrange equation. In this context, we shall rediscover the preconditioned algebraic conjugate gradient method for the discretised problem. The benefit of the connection of those concepts will be illustrated by a numerical experiment.

View Article and Find Full Text PDF

Predicting defect stability and annealing kinetics in two-dimensional PtSeusing steepest entropy ascent quantum thermodynamics.

J Phys Condens Matter

December 2022

Materials Science Engineering Department, Virginia Tech, Blacksburg, VA 24061, United States of America.

The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework was used to calculate the stability of a collection of point defects in 2D PtSeand predict the kinetics with which defects rearrange during thermal annealing. The framework provides a non-equilibrium, ensemble-based framework with a self-consistent link between mechanics (both quantum and classical) and thermodynamics. It employs an equation of motion derived from the principle of steepest entropy ascent (maximum entropy production) to predict the time evolution of a set of occupation probabilities that define the states of a system undergoing a non-equilibrium process.

View Article and Find Full Text PDF

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!