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Cuomo Salvatore (University of Naples Federico II, Italy), Galletti Ardelio (Parthenope University of Naples, Italy), Marcellino Livia (Parthenope University of Naples, Italy), Farina Raffaele (Centro Euro-Mediterraneo sui Cambiamenti Climatici)
An error estimate of Gaussian Recursive Filter in 3Dvar problem
Annals of Computer Science and Information Systems, 2014, vol. 2, s. 587 - 595, rys., tab., bibliogr. 27 poz.
Słowa kluczowe
Macierze, Analiza matematyczna, Estymacja
Matrix, Mathematical analysis, Estimation
Computational kernel of the three-dimensional variational data assimilation (3D-Var) problem is a linear system, generally solved by means of an iterative method. The most costly part of each iterative step is a matrix-vector product with a very large covariance matrix having Gaussian correlation structure. This operation may be interpreted as a Gaussian convolution, that is a very expensive numerical kernel. Recursive Filters (RFs) are a well known way to approximate the Gaussian convolution and are intensively applied in the meteorology, in the oceanography and in forecast models. In this paper, we deal with an oceanographic 3D-Var data assimilation scheme, named OceanVar, where the linear system is solved by using the Conjugate Gradient (GC) method by replacing, at each step, the Gaussian convolution with RFs. Here we give theoretical issues on the discrete convolution approximation with a first order (1st-RF) and a third order (3rd-RF) recursive filters. Numerical experiments confirm given error bounds and show the benefits, in terms of accuracy and performance, of the 3-rd RF.(original abstract)
Pełny tekst
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