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Sparse Recovery Using Sparse Matrices [PDF]
Proceedings of the IEEE, 2010 In this paper, we survey algorithms for sparse recovery problems that are based on sparse random matrices. Such matrices has several attractive properties: they support algorithms with low computational complexity, and make it easy to perform incremental updates to signals.
Piotr Indyk, Anna Gilbert
exaly +5 more sources
Block Iterators for Sparse Matrices [PDF]
Annals of computer science and information systems, 2016 Finding an optimal block size for a given sparse matrix forms an important problem for storage formats that partition matrices into uniformly-sized blocks. Finding a solution to this problem can take a significant amount of time, which, effectively, may negate the benefits that such a format brings into sparse-matrix computations.
Daniel Langr +2 more
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A note on the multiplication of sparse matrices
Open Computer Science, 2014 AbstractWe present a practical algorithm for multiplication of two sparse matrices. In fact if A and B are two matrices of size n with m 1 and m 2 non-zero elements respectively, then our algorithm performs O(min{m 1 n, m 2 n, m 1 m 2}) multiplications and O(k) additions where k is the number of non-zero elements in the tiny matrices that are obtained ...
Borna Keivan, Fard Sohrab
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Random matrices and random graphs* [PDF]
ESAIM: Proceedings and Surveys, 2023 We collect recent results on random matrices and random graphs. The topics covered are: fluctuations of the empirical measure of random matrices, finite-size effects of algorithms involving random matrices, characteristic polynomial of sparse matrices ...
Capitaine Mireille +4 more
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Subset Selection in Sparse Matrices [PDF]
SIAM Journal on Optimization, 2020 In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using mainly tools from discrete geometry, we show that some sparsity conditions on the original data matrix allow us ...
Alberto Del Pia +2 more
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Sparse random block matrices [PDF]
Journal of Physics A: Mathematical and Theoretical, 2022 Abstract The spectral moments of ensembles of sparse random block matrices are analytically evaluated in the limit of large order. The structure of the sparse matrix corresponds to the Erdös–Renyi random graph. The blocks are i.i.d. random matrices of the classical ensembles GOE or GUE. The moments are evaluated for finite or infinite
Giovanni M Cicuta, Mario Pernici
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Sparse block-structured random matrices: universality
Journal of Physics: Complexity, 2023 We study ensembles of sparse block-structured random matrices generated from the adjacency matrix of a Erdös–Renyi random graph with N vertices of average degree Z , inserting a real symmetric d × d random block at each non-vanishing entry. We consider
Giovanni M Cicuta, Mario Pernici
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Nihon Kikai Gakkai ronbunshu, 2023 NV (Noise and Vibration) performance is determined by the influence of all components constituting a whole structure. It is difficult to design NV performance efficiently because the structural modification of a certain component affects the performance ...
Masashi INABA, Yuichi MATSUMURA
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On the Rank of Random Sparse Matrices [PDF]
Combinatorics, Probability and Computing, 2009 We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This allows us to obtain an exact estimate for the co-rank.
Kevin P. Costello, Van H. Vu
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The Chunks and Tasks Matrix Library
SoftwareX, 2022 We present a C++ header-only parallel sparse matrix library, based on sparse quadtree representation of matrices using the Chunks and Tasks programming model.
Emanuel H. Rubensson +3 more
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