Variational fitting of the Fock exchange potential with modified Cholesky decomposition

2020 ◽  
Vol 153 (13) ◽  
pp. 134112
Author(s):  
Jesús Naín Pedroza-Montero ◽  
Francisco Antonio Delesma ◽  
José Luis Morales ◽  
Patrizia Calaminici ◽  
Andreas M. Köster
Keyword(s):  
Cholesky Decomposition ◽  
Exchange Potential ◽  
Modified Cholesky Decomposition

Asymmetric Density Fitting with Modified Cholesky Decomposition Applied to Second-Order Electron Propagator

2020 ◽  
Vol 16 (3) ◽  
pp. 1597-1605
Author(s):  
Juan Felipe Huan Lew-Yee ◽  
Roberto Flores-Moreno ◽  
José Luis Morales ◽  
Jorge M. del Campo
Keyword(s):  
Cholesky Decomposition ◽  
Second Order ◽  
Electron Propagator ◽  
Modified Cholesky Decomposition ◽  
Density Fitting

scholarly journals A Maximum Likelihood Ensemble Filter via a Modified Cholesky Decomposition for Non-Gaussian Data Assimilation

Sensors ◽  
2020 ◽  
Vol 20 (3) ◽  
pp. 877 ◽  
Author(s):  
Elias David Nino-Ruiz ◽  
Alfonso Mancilla-Herrera ◽  
Santiago Lopez-Restrepo ◽  
Olga Quintero-Montoya
Keyword(s):  
Maximum Likelihood ◽  
General Circulation ◽  
Circulation Model ◽  
Cholesky Decomposition ◽  
Practical Implementation ◽  
Square Root ◽  
Background Error ◽  
Modified Cholesky Decomposition ◽  
Highly Nonlinear ◽  
Maximum Likelihood Ensemble Filter

This paper proposes an efficient and practical implementation of the Maximum Likelihood Ensemble Filter via a Modified Cholesky decomposition (MLEF-MC). The method works as follows: via an ensemble of model realizations, a well-conditioned and full-rank square-root approximation of the background error covariance matrix is obtained. This square-root approximation serves as a control space onto which analysis increments can be computed. These are calculated via Line-Search (LS) optimization. We theoretically prove the convergence of the MLEF-MC. Experimental simulations were performed using an Atmospheric General Circulation Model (AT-GCM) and a highly nonlinear observation operator. The results reveal that the proposed method can obtain posterior error estimates within reasonable accuracies in terms of ℓ − 2 error norms. Furthermore, our analysis estimates are similar to those of the MLEF with large ensemble sizes and full observational networks.

MODIFIED CHOLESKY DECOMPOSITION FOR SOLVING THE MOMENT MATRIX IN THE RADIAL POINT INTERPOLATION METHOD

2014 ◽  
Vol 11 (06) ◽  
pp. 1350088 ◽  
Author(s):  
DOMEN STADLER ◽  
DAMJAN ČELIČ ◽  
ANDREJ LIPEJ ◽  
FRANC KOSEL
Keyword(s):  
Interpolation Method ◽  
Cholesky Decomposition ◽  
Decomposition Technique ◽  
Moment Matrix ◽  
Radial Point Interpolation Method ◽  
Modified Cholesky Decomposition ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
The Moment

The radial point interpolation method is frequently employed in numerical computations. It can be used to interpolate scattered data, as shape functions in meshless methods and mesh deformation scheme, etc. The main problem in calculating the radial point interpolation is solving the moment matrix of the interpolation scheme, which is usually done with LU decomposition. A new decomposition technique based on the Cholesky decomposition is introduced in this paper. A comparison of the error, the consumed time and the results between the new decomposition technique and the LU method is presented for two different numerical methods.

Sign in / Sign up

Export Citation Format

Share Document