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

Introduction to Scalers01:21

Introduction to Scalers

Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, "a class period lasts 50 min," or "the gas tank in my car holds 65 L," or "the distance between the two posts is 100 m." A physical quantity that can be specified completely in this manner is called a scalar quantity. The word "scalar" is a synonym for "number." Time, mass, distance, length, volume, temperature, and energy are some examples of scalar quantities.
Scalar...
Gaussian Elimination: Problem Solving01:30

Gaussian Elimination: Problem Solving

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...
Chebyshev's Theorem to Interpret Standard Deviation01:15

Chebyshev's Theorem to Interpret Standard Deviation

Chebyshev’s theorem, also known as Chebyshev’s Inequality, states that the proportion of values of a dataset for K standard deviation is calculated using the equation:
Quadratic Models01:23

Quadratic Models

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...
Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an organic...
Linearization and Approximation01:26

Linearization and Approximation

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...

You might also read

Related Articles

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

Sort by
Same author

Tuning Connectivity in Hybrid Organic-Inorganic Antimony Halides through Reactant Concentration Effects.

Inorganic chemistry·2026
Same author

A Benchmark and Basis-Set Extrapolation Study of Hyperfine Coupling Constants from the Random Phase Approximation and σ-Functionals.

The journal of physical chemistry. A·2026
Same author

A detailed comparison of ΔSCF methods with the constraint-based orbital-optimized excited state method.

Communications chemistry·2026
Same author

Formulation of an Efficient <math><mi>O</mi></math>(<i>M</i><sup>4</sup>)-Scaling Explicitly Correlated MP2-F12 Correction by Combining Numerical Quadrature with Density Fitting and CABS-RI.

Journal of chemical theory and computation·2026
Same author

Automated Discovery of Reactive Events via Hypergraph Mining of Ab Initio Atomistic Simulations.

Journal of chemical theory and computation·2026
Same author

Quantum chemistry - from the first steps to linear-scaling electronic structure methods.

Pure and applied chemistry. Chimie pure et appliquee·2025

Related Experiment Video

Updated: Jul 10, 2026

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
06:52

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Published on: September 17, 2019

Linear-scaling Cholesky decomposition.

Sabine Schweizer1, Jörg Kussmann, Bernd Doser

  • 1Institut für Physikalische und Theoretische Chemie, Universität Tübingen, Auf der Morgenstelle 8, D-72076 Tübingen, Germany.

Journal of Computational Chemistry
|November 14, 2007
PubMed
Summary

We developed efficient linear-scaling algorithms for Cholesky decomposition and matrix inversion. These methods significantly improve computational performance for large, complex molecular systems, offering a valuable tool for computational chemistry.

More Related Videos

A Three-Dimensional Digital Model for Early Diagnosis of Hepatic Fibrosis Based on Magnetic Resonance Elastography
06:09

A Three-Dimensional Digital Model for Early Diagnosis of Hepatic Fibrosis Based on Magnetic Resonance Elastography

Published on: July 21, 2023

Related Experiment Videos

Last Updated: Jul 10, 2026

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
06:52

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Published on: September 17, 2019

A Three-Dimensional Digital Model for Early Diagnosis of Hepatic Fibrosis Based on Magnetic Resonance Elastography
06:09

A Three-Dimensional Digital Model for Early Diagnosis of Hepatic Fibrosis Based on Magnetic Resonance Elastography

Published on: July 21, 2023

Area of Science:

  • Computational Chemistry
  • Numerical Linear Algebra
  • Quantum Chemistry

Background:

  • Cholesky decomposition and matrix inversion are fundamental operations in computational chemistry.
  • Standard algorithms exhibit unfavorable scaling for large systems, limiting computational feasibility.
  • Efficient methods are crucial for analyzing large molecular systems in electronic structure calculations.

Purpose of the Study:

  • To present novel linear-scaling routines for Cholesky decomposition and matrix inversion.
  • To demonstrate the applicability of these routines to large molecular systems.
  • To compare the performance and scaling of the new routines against established methods.

Main Methods:

  • Development of linear-scaling algorithms for Cholesky decomposition.
  • Implementation of algorithms for matrix inversion.
  • Application to the overlap matrix of DNA, amylose fragments, and linear alkanes.
  • Comparison with standard LAPACK routines for efficiency and scaling.

Main Results:

  • The developed routines achieve linear scaling for Cholesky decomposition and matrix inversion.
  • Successful application to matrices as large as 21,442 x 21,442.
  • Demonstrated superior efficiency and scaling behavior compared to standard LAPACK routines.

Conclusions:

  • The new linear-scaling routines provide a significant computational advantage for large-scale problems.
  • These methods are effective for inverting overlap matrices in molecular systems.
  • The publicly available routines offer a practical solution for accelerating computational chemistry workflows.