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.

Analytical energy gradients for second-order multireference perturbation theory using density fitting

2013 ◽  
Vol 138 (10) ◽  
pp. 104104 ◽  
Author(s):  
Werner Győrffy ◽  
Toru Shiozaki ◽  
Gerald Knizia ◽  
Hans-Joachim Werner
Keyword(s):  
Perturbation Theory ◽  
Second Order ◽  
Multireference Perturbation Theory ◽  
Density Fitting

Orbital-optimized linearized coupled-cluster doubles with density-fitting and Cholesky decomposition approximations: an efficient implementation

2016 ◽  
Vol 18 (16) ◽  
pp. 11362-11373 ◽  
Author(s):  
Uğur Bozkaya
Keyword(s):  
Cholesky Decomposition ◽  
Efficient Implementation ◽  
Coupled Cluster ◽  
Density Fitting

An efficient implementation of the orbital-optimized linearized coupled-cluster double method with the density-fitting (DF-OLCCD) and Cholesky decomposition (CD-OLCCD) approximations is presented.

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