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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
https://doi.org/10.5194/gmd-2016-204
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Development and technical paper
21 Sep 2016
Review status
A revision of this discussion paper for further review has not been submitted.
Technical Note: Improving the computational efficiency of sparse matrix multiplication in linear atmospheric inverse problems
Vineet Yadav1 and Anna M. Michalak2 1Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, 91011, USA
2Department of Global Ecology, Carnegie Institution for Science, Stanford, California, 94305, USA
Abstract. Matrix multiplication of two sparse matrices is a fundamental operation in linear Bayesian inverse problems for computing covariance matrices of observations and a posteriori uncertainties. Applications of sparse-sparse matrix multiplication algorithms for specific use-cases in such inverse problems remain unexplored. Here we present a hybrid-parallel sparse-sparse matrix multiplication approach that is more efficient by a third in terms of execution time and operation count relative to standard sparse matrix multiplication algorithms available in most libraries. Two modifications of this hybrid-parallel algorithm are also proposed for the types of operations typical of atmospheric inverse problems, which further reduce the cost of sparse matrix multiplication by yielding only upper triangular and/or dense matrices.

Citation: Yadav, V. and Michalak, A. M.: Technical Note: Improving the computational efficiency of sparse matrix multiplication in linear atmospheric inverse problems, Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2016-204, in review, 2016.
Vineet Yadav and Anna M. Michalak
Interactive discussionStatus: closed (peer review stopped)
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
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RC1: 'Review of ``Technical Note: Improving the computational efficiency of sparse matrix multiplication in linear atmospheric inversion'' by Vineet Yadav, Anna M. Michalak', Anonymous Referee #1, 21 Oct 2016 Printer-friendly Version 
 
RC2: 'manuscript review for V Yadav et al.', Anonymous Referee #2, 24 Jan 2017 Printer-friendly Version 
Vineet Yadav and Anna M. Michalak
Vineet Yadav and Anna M. Michalak

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Short summary
Multiplication of two matrices that consists of few non-zero entries is a fundamental operation in problems that involve estimation of greenhouse gas fluxes from atmospheric measurements. To increase computational efficiency of estimating these quantities, modification of the standard matrix multiplication algorithm for multiplying these matrices is proposed in this research.
Multiplication of two matrices that consists of few non-zero entries is a fundamental operation...
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