On variable ordination of modified Cholesky decomposition for estimating time‐varying covariance matrices

2019 ◽  
Vol 88 (3) ◽  
pp. 616-641 ◽  
Author(s):  
Xiaoning Kang ◽  
Xinwei Deng ◽  
Kam‐Wah Tsui ◽  
Mohsen Pourahmadi
Keyword(s):  
Cholesky Decomposition ◽  
Covariance Matrices ◽  
Time Varying ◽  
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.

scholarly journals Analytical SLAM without linearization

2017 ◽  
Vol 36 (13-14) ◽  
pp. 1554-1578 ◽  
Author(s):  
Feng Tan ◽  
Winfried Lohmiller ◽  
Jean-Jacques Slotine
Keyword(s):  
Convergence Rates ◽  
Linear Time ◽  
Classical Problem ◽  
Covariance Matrices ◽  
Time Varying ◽  
Extended Kalman Filtering ◽  
Independence Property ◽  
Localization And Mapping ◽  
2D And 3D ◽  
Advanced Version

This paper solves the classical problem of simultaneous localization and mapping (SLAM) in a fashion that avoids linearized approximations altogether. Based on the creation of virtual synthetic measurements, the algorithm uses a linear time-varying Kalman observer, bypassing errors and approximations brought by the linearization process in traditional extended Kalman filtering SLAM. Convergence rates of the algorithm are established using contraction analysis. Different combinations of sensor information can be exploited, such as bearing measurements, range measurements, optical flow, or time-to-contact. SLAM-DUNK, a more advanced version of the algorithm in global coordinates, exploits the conditional independence property of the SLAM problem, decoupling the covariance matrices between different landmarks and reducing computational complexity to O(n). As illustrated in simulations, the proposed algorithm can solve SLAM problems in both 2D and 3D scenarios with guaranteed convergence rates in a full nonlinear context.

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
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