A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation

We propose a limited-memory quasi-Newton method using the bad Broyden update and apply it to the nonlinear equations that must be solved to determine the effective Fermi momentum in the weighted density approximation for the exchange energy density functional. This algorithm has advantages for nonli...

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Main Authors:	Matthew Chan, Rogelio Cuevas-Saavedra, Debajit Chakraborty, Paul W. Ayers
Format:	Article
Language:	English
Published:	MDPI AG 2017-09-01
Series:	Computation
Subjects:	weighted density approximation limited memory quasi-Newton method nonlinear systems of equations bad Broyden method density functional theory exchange energy density functional
Online Access:	https://www.mdpi.com/2079-3197/5/4/42

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spelling	doaj-7991527fec524eae8903e5285eff581b2020-11-25T00:10:11ZengMDPI AGComputation2079-31972017-09-01544210.3390/computation5040042computation5040042A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density ApproximationMatthew Chan0Rogelio Cuevas-Saavedra1Debajit Chakraborty2Paul W. Ayers3Department of Chemistry & Chemical Biology; McMaster University, Hamilton, ON L8S 4L8, CanadaDepartment of Chemistry & Chemical Biology; McMaster University, Hamilton, ON L8S 4L8, CanadaDepartment of Chemistry & Chemical Biology; McMaster University, Hamilton, ON L8S 4L8, CanadaDepartment of Chemistry & Chemical Biology; McMaster University, Hamilton, ON L8S 4L8, CanadaWe propose a limited-memory quasi-Newton method using the bad Broyden update and apply it to the nonlinear equations that must be solved to determine the effective Fermi momentum in the weighted density approximation for the exchange energy density functional. This algorithm has advantages for nonlinear systems of equations with diagonally dominant Jacobians, because it is easy to generalize the method to allow for periodic updates of the diagonal of the Jacobian. Systematic tests of the method for atoms show that one can determine the effective Fermi momentum at thousands of points in less than fifteen iterations.https://www.mdpi.com/2079-3197/5/4/42weighted density approximationlimited memory quasi-Newton methodnonlinear systems of equationsbad Broyden methoddensity functional theoryexchange energy density functional
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Matthew Chan Rogelio Cuevas-Saavedra Debajit Chakraborty Paul W. Ayers
spellingShingle	Matthew Chan Rogelio Cuevas-Saavedra Debajit Chakraborty Paul W. Ayers A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation Computation weighted density approximation limited memory quasi-Newton method nonlinear systems of equations bad Broyden method density functional theory exchange energy density functional
author_facet	Matthew Chan Rogelio Cuevas-Saavedra Debajit Chakraborty Paul W. Ayers
author_sort	Matthew Chan
title	A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation
title_short	A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation
title_full	A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation
title_fullStr	A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation
title_full_unstemmed	A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation
title_sort	diagonally updated limited-memory quasi-newton method for the weighted density approximation
publisher	MDPI AG
series	Computation
issn	2079-3197
publishDate	2017-09-01
description	We propose a limited-memory quasi-Newton method using the bad Broyden update and apply it to the nonlinear equations that must be solved to determine the effective Fermi momentum in the weighted density approximation for the exchange energy density functional. This algorithm has advantages for nonlinear systems of equations with diagonally dominant Jacobians, because it is easy to generalize the method to allow for periodic updates of the diagonal of the Jacobian. Systematic tests of the method for atoms show that one can determine the effective Fermi momentum at thousands of points in less than fifteen iterations.
topic	weighted density approximation limited memory quasi-Newton method nonlinear systems of equations bad Broyden method density functional theory exchange energy density functional
url	https://www.mdpi.com/2079-3197/5/4/42
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A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation

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