Technical Note: Improving the computational efficiency of sparse matrix multiplication in linear atmospheric inverse problems

Vineet Yadav^{1} and Anna M. Michalak^{2}^{1}Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, 91011, USA ^{2}Department 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., doi:10.5194/gmd-2016-204, in review, 2016.