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Related Concept Videos

Density00:56

Density

Density is an important characteristic of substances, crucial in determining whether an object sinks or floats in a fluid. Its SI unit is kg/m3, and its cgs unit is g/cm3. The density of an object helps in identifying its composition, and also reveals information about the phase of the matter and its substructure. The densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. However, gases have much lower densities than liquids and...
Density and Archimedes' Principle01:05

Density and Archimedes' Principle

When a lump of clay is dropped into water, it sinks. But if the same lump of clay is molded into the shape of a boat, it starts to float. Because of its shape, the clay boat displaces more water than the lump and experiences a greater buoyant force, even though its mass is the same. The same holds true for steel ships. The average density of an object majorly determines if the object will float. If an object's average density is less than that of the surrounding fluid, it will float. The reason...
Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
Estimation of the Physical Quantities01:05

Estimation of the Physical Quantities

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...

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Updated: Jun 19, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

Robust and efficient density fitting.

Víctor D Domínguez-Soria1, Gerald Geudtner, José Luis Morales

  • 1Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, México DF 07000, Mexico.

The Journal of Chemical Physics
|October 2, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces an iterative method using conjugate gradient and quasi-Newton preconditioners for solving linear equations in density fitting. The new parallel algorithm matches standard methods in accuracy for large systems.

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Area of Science:

  • Computational chemistry
  • Numerical analysis
  • Linear algebra

Background:

  • Density fitting is crucial for computational chemistry calculations.
  • Solving associated linear equations can be computationally intensive.
  • Existing direct methods may face scalability challenges.

Purpose of the Study:

  • To present an iterative method for solving linear systems in density fitting.
  • To incorporate automatically built quasi-Newton preconditioners.
  • To detail a parallel implementation of the proposed method.

Main Methods:

  • Iterative solution of inhomogeneous linear systems.
  • Application of a conjugate gradient method.
  • Utilizing automatically constructed quasi-Newton preconditioners.
  • Parallel implementation for enhanced performance.

Main Results:

  • The proposed iterative method effectively solves linear equations for density fitting.
  • Benchmark calculations were performed on large systems (up to 35,000 auxiliary functions).
  • The parallel implementation demonstrates computational viability.

Conclusions:

  • The new iterative method provides accurate solutions comparable to direct methods.
  • The approach is suitable for large-scale density fitting problems.
  • The parallel implementation offers an efficient alternative for computational chemistry.