scholarly journals Review of ``Technical Note: Improving the computational efficiency of sparse matrix multiplication in linear atmospheric inversion'' by Vineet Yadav, Anna M. Michalak

2016 ◽  
Author(s):  
Anonymous
Keyword(s):  
Computational Efficiency ◽  
Sparse Matrix ◽  
Matrix Multiplication ◽  
Technical Note ◽  
Atmospheric Inversion

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

2016 ◽  
Author(s):  
Vineet Yadav ◽  
Anna M. Michalak
Keyword(s):  
Inverse Problems ◽  
Sparse Matrix ◽  
Sparse Matrices ◽  
Matrix Multiplication ◽  
Technical Note ◽  
Covariance Matrices ◽  
A Posteriori ◽  
Bayesian Inverse Problems ◽  
Dense Matrices ◽  
The Cost

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.

scholarly journals Sparse matrix multiplication: The distributed block-compressed sparse row library

2014 ◽  
Vol 40 (5-6) ◽  
pp. 47-58 ◽  
Author(s):  
Urban Borštnik ◽  
Joost VandeVondele ◽  
Valéry Weber ◽  
Jürg Hutter
Keyword(s):  
Sparse Matrix ◽  
Matrix Multiplication ◽  
Compressed Sparse Row

Unleashing the performance of bmSparse for the sparse matrix multiplication in GPUs

2021 ◽  
Author(s):  
Gonzalo Berger ◽  
Manuel Freire ◽  
Renzo Marini ◽  
Ernesto Dufrechou ◽  
Pablo Ezzatti
Keyword(s):  
Sparse Matrix ◽  
Matrix Multiplication

scholarly journals Technical Note: Improving computational efficiency in large linear inverse problems: an example from carbon dioxide flux estimation

2012 ◽  
Vol 5 (4) ◽  
pp. 3325-3342
Author(s):  
V. Yadav ◽  
A. M. Michalak
Keyword(s):  
Carbon Dioxide ◽  
Inverse Problems ◽  
Computational Efficiency ◽  
Optimization Problems ◽  
Temporal Distribution ◽  
Carbon Dioxide Flux ◽  
Technical Note ◽  
Sensitivity Matrix ◽  
Direct Computation ◽  
Spatio Temporal

Abstract. Addressing a variety of questions within Earth science disciplines entails the inference of the spatio-temporal distribution of parameters of interest based on observations of related quantities. Such estimation problems often represent inverse problems that are formulated as linear optimization problems. Computational limitations arise when the number of observations and/or the size of the discretized state space become large, especially if the inverse problem is formulated in a probabilistic framework and therefore aims to assess the uncertainty associated with the estimates. This work proposes two approaches to lower the computational costs and memory requirements for large linear space-time inverse problems, taking the Bayesian approach for estimating carbon dioxide (CO2) emissions and uptake (a.k.a. fluxes) as a prototypical example. The first algorithm can be used to efficiently multiply two matrices, as long as one can be expressed as a Kronecker product of two smaller matrices, a condition that is typical when multiplying a sensitivity matrix by a covariance matrix in the solution of inverse problems. The second algorithm can be used to compute a posteriori uncertainties directly at aggregated spatio-temporal scales, which are the scales of most interest in many inverse problems. Both algorithms have significantly lower memory requirements and computational complexity relative to direct computation of the same quantities (O(n2.5) vs. O(n3)). For an examined benchmark problem, the two algorithms yielded a three and six order of magnitude increase in computational efficiency, respectively, relative to direct computation of the same quantities. Sample computer code is provided for assessing the computational and memory efficiency of the proposed algorithms for matrices of different dimensions.

Optimization of GPU-based Sparse Matrix Multiplication for Large Sparse Networks

2020 ◽  
Author(s):  
Jeongmyung Lee ◽  
Seokwon Kang ◽  
Yongseung Yu ◽  
Yong-Yeon Jo ◽  
Sang-Wook Kim ◽  
...  
Keyword(s):  
Sparse Matrix ◽  
Matrix Multiplication ◽  
Sparse Networks
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