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Large-scale Sparse Inverse Covariance Matrix Estimation
SIAM Journal on Scientific Computing, 2019The estimation of large sparse inverse covariance matrices is a ubiquitous statistical problem in many application areas such as mathematical finance, geology, health, and many others.
M. Bollhöfer +3 more
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Symbolic Matrix Multiplication for Multithreaded Sparse GEMM Utilizing Sparse Matrix Formats
2018 International Conference on High Performance Computing & Simulation (HPCS), 2018Sparse matrices are exploited in many problems from scientific computing and, thus, their efficient implementation is crucial for the overall performance of the problems. Three sparse matrix formats, such as Compressed Sparse Row Storage, Block Sparse Row Storage and Ellpack-Itpack, have been proposed to support an efficient storage and access to ...
Marcel Richter, Gudula Runger
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The 23rd IEEE Conference on Decision and Control, 1984
Numerical linear algebra plays a vital role in all parts of computational mathematics, such as differential equations and optimization, and in many application areas, such as control theory. Large systems in these areas generally lead to linear algebra problems involving large sparse matrices (i.e., matrices of large dimension, but whose entries are ...
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Numerical linear algebra plays a vital role in all parts of computational mathematics, such as differential equations and optimization, and in many application areas, such as control theory. Large systems in these areas generally lead to linear algebra problems involving large sparse matrices (i.e., matrices of large dimension, but whose entries are ...
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ACM SIGNUM Newsletter, 1982
The development, analysis and production of algorithms in sparse linear algebra often requires the use of test problems to demonstrate the effectiveness and applicability of the algorithms. Many algorithms have been developed in the context of specific application areas and have been tested in the context of sets of test problems collected by the ...
Iain Duff +3 more
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The development, analysis and production of algorithms in sparse linear algebra often requires the use of test problems to demonstrate the effectiveness and applicability of the algorithms. Many algorithms have been developed in the context of specific application areas and have been tested in the context of sets of test problems collected by the ...
Iain Duff +3 more
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1988
In view of the previously derived N3 dependence of the long operations count on the number of equations to be solved via Gaussian elimination, computation time can be expected to increase significantly as larger circuits with more nodes are considered. As a consequence, much attention has been focused on taking advantage of sparsity in nodal admittance
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In view of the previously derived N3 dependence of the long operations count on the number of equations to be solved via Gaussian elimination, computation time can be expected to increase significantly as larger circuits with more nodes are considered. As a consequence, much attention has been focused on taking advantage of sparsity in nodal admittance
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Sparse matrix storage revisited
Proceedings of the 2nd conference on Computing frontiers, 2005In this paper, we consider alternate ways of storing a sparse matrix and their effect on computational speed. They involve keeping both the indices and the non-zero elements in the sparse matrix in a single data structure. These schemes thus help reduce memory system misses that occur when the usual indexing based storage schemes are used to store ...
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I/O-Optimal Cache-Oblivious Sparse Matrix-Sparse Matrix Multiplication
2022 IEEE International Parallel and Distributed Processing Symposium (IPDPS), 2022Gleinig, Niels +2 more
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