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This article is cited in 1 scientific paper (total in 1 paper)
Computational mathematics
An efficient truncated SVD of large matrices based on the low-rank approximation for inverse geophysical problems
S. A. Solovyeva, S. Tordeuxbc a Institute of Petroleum Geology and Geophysics SB RAS, pr. Koptyuga, 3, 630090, Novosibirsk, Russia
b Inria Bordeaux Sud-Ouest, Equipe-Projet Magique-3D IPRA-LMA
c Université de Pau et des Pays de l'Adour, BP 1155, 64013 Pau Cedex, Université de Pau, France
Abstract:
In this paper, we propose a new algorithm
to compute a truncated singular value decomposition (T-SVD) of the
Born matrix based on a low-rank arithmetic. This algorithm is tested
in the context of acoustic media. Theoretical background to the
low-rank SVD method is presented: the Born matrix of an acoustic
problem can be approximated by a low-rank approximation derived
thanks to a kernel independent multipole expansion. The new
algorithm to compute T-SVD approximation consists of four steps,
and they are described in detail. The largest singular values and
their left and right singular vectors can be approximated
numerically without performing any operation with the full matrix.
The low-rank approximation is computed due to a dynamic panel
strategy of cross approximation (CA) technique.
At the end of the paper, we present a numerical experiment to illustrate the efficiency and precision of the algorithm proposed.
Keywords:
Born matrix, SVD algorithm, cross approximation (CA), low-rank approximation, high-performance computing, parallel computations.
Received July 14, 2015, published September 22, 2015
Citation:
S. A. Solovyev, S. Tordeux, “An efficient truncated SVD of large matrices based on the low-rank approximation for inverse geophysical problems”, Sib. Èlektron. Mat. Izv., 12 (2015), 592–609
Linking options:
https://www.mathnet.ru/eng/semr614 https://www.mathnet.ru/eng/semr/v12/p592
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