Technical Note: Improving the computational efficiency of sparse matrix multiplication in linear atmospheric inverse problems
Vineet Yadav1 and Anna M. Michalak21Jet 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.
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.