Technical Note: Improving the computational efficiency of sparse matrix...

Yadav, V., and A. M. Michalak (2016), Technical Note: Improving the computational efficiency of sparse matrix multiplication in linear atmospheric inverse problems, Geosci. Model. Dev., doi:10.5194/gmd-2016-204.

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.

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Carbon Cycle & Ecosystems Program (CCEP)