Numerical Effects of the Gaussian Recursive Filters in Solving Linear Systems in the 3Dvar Case Study
Year: 2017
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 3 : pp. 520–540
Abstract
In many applications, the Gaussian convolution is approximately computed by means of recursive filters, with a significant improvement of computational efficiency. We are interested in theoretical and numerical issues related to such an use of recursive filters in a three-dimensional variational data assimilation (3Dvar) scheme as it appears in the software OceanVar. In that context, the main numerical problem consists in solving large linear systems with high efficiency, so that an iterative solver, namely the conjugate gradient method, is equipped with a recursive filter in order to compute matrix-vector multiplications that in fact are Gaussian convolutions. Here we present an error analysis that gives effective bounds for the perturbation on the solution of such linear systems, when is computed by means of recursive filters. We first prove that such a solution can be seen as the exact solution of a perturbed linear system. Then we study the related perturbation on the solution and we demonstrate that it can be bounded in terms of the difference between the two linear operators associated to the Gaussian convolution and the recursive filter, respectively. Moreover, we show through numerical experiments that the error on the solution, which exhibits a kind of edge effect, i.e. most of the error is localized in the first and last few entries of the computed solution, is due to the structure of the difference of the two linear operators.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2017.m1528
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 3 : pp. 520–540
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
-
Data Assimilation for Parameter Estimation in Economic Modelling
Nadler, Philip | Arcucci, Rossella | Guo, Yi-Ke2019 15th International Conference on Signal-Image Technology & Internet-Based Systems (SITIS), (2019), P.649
https://doi.org/10.1109/SITIS.2019.00106 [Citations: 5] -
A Gaussian Recursive Filter Parallel Implementation with Overlapping
De Luca, Pasquale | Galletti, Ardelio | Marcellino, Livia2019 15th International Conference on Signal-Image Technology & Internet-Based Systems (SITIS), (2019), P.641
https://doi.org/10.1109/SITIS.2019.00105 [Citations: 13] -
Hybrid Data Assimilation: An Ensemble-Variational Approach
Lim, Edward M. | Molina Solana, Miguel | Pain, Christopher | Guo, Yi-Ke | Arcucci, Rossella2019 15th International Conference on Signal-Image Technology & Internet-Based Systems (SITIS), (2019), P.633
https://doi.org/10.1109/SITIS.2019.00104 [Citations: 2] -
Computational Science – ICCS 2022
A GPU-Based Algorithm for Environmental Data Filtering
De Luca, Pasquale | Galletti, Ardelio | Marcellino, Livia2022
https://doi.org/10.1007/978-3-031-08760-8_4 [Citations: 2] -
A GPU Parallel Algorithm for Image Denoising Based on Wavelet Transform Coefficients Thresholding
Galletti, Ardelio | Marcellino, Livia | Russo, Luigi2018 14th International Conference on Signal-Image Technology & Internet-Based Systems (SITIS), (2018), P.485
https://doi.org/10.1109/SITIS.2018.00080 [Citations: 1] -
Computational Science – ICCS 2020
Accelerated Gaussian Convolution in a Data Assimilation Scenario
De Luca, Pasquale | Galletti, Ardelio | Giunta, Giulio | Marcellino, Livia2020
https://doi.org/10.1007/978-3-030-50433-5_16 [Citations: 9] -
Estimating Snow Depth Using Multi-Source Data Fusion Based on the D-InSAR Method and 3DVAR Fusion Algorithm
Liu, Yang | Li, Lanhai | Yang, Jinming | Chen, Xi | Hao, JianshengRemote Sensing, Vol. 9 (2017), Iss. 11 P.1195
https://doi.org/10.3390/rs9111195 [Citations: 20] -
GPU-CUDA Implementation of the Third Order Gaussian Recursive Filter
De Luca, Pasquale | Galletti, Ardelio | Marcellino, LiviaSN Computer Science, Vol. 3 (2022), Iss. 1
https://doi.org/10.1007/s42979-021-00960-7 [Citations: 0] -
An epidemiological modelling approach for COVID-19 via data assimilation
Nadler, Philip | Wang, Shuo | Arcucci, Rossella | Yang, Xian | Guo, YikeEuropean Journal of Epidemiology, Vol. 35 (2020), Iss. 8 P.749
https://doi.org/10.1007/s10654-020-00676-7 [Citations: 37]