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Semi-deterministic Sparse Matrix for Low Complexity Compressive Sampling
2017
KSII Transactions on Internet and Information Systems
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Only the row index is selected at random and the positions of the entries of each row are determined by a deterministic sequence. ...
The construction of completely random sensing matrices of Compressive Sensing requires a large number of random numbers while that of deterministic sensing operators often needs complex mathematical operations ...
Besieds, because of dense matrix is not suitable for processing, the sparse version of random and deterministic sensing matrices have also been investigated [10] , [11] . ...
doi:10.3837/tiis.2017.05.009
fatcat:z3xatzs3wbfs3p5cdxenvuoauu
Efficient computation of the characteristic polynomial
2005
Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05
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We deal with the computation of the characteristic polynomial of dense matrices over word size finite fields and over the integers. ...
We use these results as a basis for the computation of the characteristic polynomial of integer matrices. We first use early termination and Chinese remaindering for dense matrices. ...
We applied our algorithm for the computation of the integer characteristic polynomial in two ways: a simple deterministic use of Chinese remaindering for dense matrix computations, and a probabilistic ...
doi:10.1145/1073884.1073905
dblp:conf/issac/DumasPW05
fatcat:pswfsqhp3rcqzn6sr5q6jsfnri
An Adaptable Fast Matrix Multiplication Algorithm, Going Beyond the Myth of Decimal War
[article]
2013
arXiv
pre-print
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In this paper we present an adaptable fast matrix multiplication (AFMM) algorithm, for two nxn dense matrices which computes the product matrix with average complexity Tavg(n) = d1d2n3 with the acknowledgement ...
Fortunately the assumptions made in this paper regarding the values in either of pre/post factor matrices can be generalized for arbitrary valued dense matrices. ...
In this paper we present an adaptable matrix multiplication algorithm, for two nxn dense matrices. ...
arXiv:1308.2400v1
fatcat:z6e562jwfve6jbptol5hmvttja
Efficient Computation of the Characteristic Polynomial
[article]
2005
arXiv
pre-print
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This article deals with the computation of the characteristic polynomial of dense matrices over small finite fields and over the integers. ...
We use these results as a basis for the computation of the characteristic polynomial of integer matrices. We first use early termination and Chinese remaindering for dense matrices. ...
Our deterministic algorithm has similar computational timings and gets faster for large matrices. ...
arXiv:cs/0501074v2
fatcat:lgyughj5ujhw3lxljtcvxikhlm
Deterministic CUR for Improved Large-Scale Data Analysis: An Empirical Study
[chapter]
2012
Proceedings of the 2012 SIAM International Conference on Data Mining
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However, these are hardly applicable to large matrices as they typically suffer from high computational costs. ...
Compared to other deterministic CUR-like methods, it provides comparable reconstruction quality but operates much faster so that it easily scales to matrices of billions of elements. ...
of mid-and large-scale as well as dense and sparse matrices. ...
doi:10.1137/1.9781611972825.59
dblp:conf/sdm/ThurauKB12
fatcat:3gocf3m5q5dnxfqjtocd7pbuwi
Mixed Monte Carlo Parallel Algorithms for Matrix Computation
[chapter]
2002
Lecture Notes in Computer Science
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Experimental results with dense and sparse matrices are presented. ...
In this paper we consider mixed (fast stochastic approximation and deterministic re nement) algorithms for Matrix Inversion (MI) and Solving Systems of Linear Equations (SLAE). ...
Further experiments are required to determine the optimal number of chains required for Monte Carlo procedures and how best to tailor together Monte Carlo and deterministic re nement procedures. ...
doi:10.1007/3-540-46080-2_63
fatcat:rlgjbzqxijct7fzw4dkbslliwq
Sparse Matrix Multiplication and Triangle Listing in the Congested Clique Model
[article]
2019
arXiv
pre-print
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Moreover, this new deterministic method for restructuring matrices may be used to restructure the adjacency matrix of input graphs, enabling faster solutions for graph related problems. ...
Our algorithmic contribution is a new deterministic method of restructuring the input matrices in a sparsity-aware manner, which assigns each node with element-wise multiplication tasks that are not necessarily ...
dimensions are determined dynamically, based on the sparsity of the input matrices. ...
arXiv:1802.04789v4
fatcat:tmvmycoeorh3lckwtzeybki4fu
Monte Carlo linear solvers with non-diagonal splitting
2010
Mathematics and Computers in Simulation
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The significance of this work lies in proposing an approach that can lead to efficient MC implementations of a wider variety of deterministic iterative processes. ...
Monte Carlo (MC) linear solvers can be considered stochastic realizations of deterministic stationary iterative processes. ...
However, N −1 is dense, and we can neither afford O(n 2 ) computation time to determine it, nor the O(n 2 ) space to store it. ...
doi:10.1016/j.matcom.2009.03.010
fatcat:73yy4pzawvberc3f6syjhtqezu
Sparse matrix multiplication and triangle listing in the Congested Clique model
2019
Theoretical Computer Science
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As applications, we show how to speed up the computation on non-dense graphs of 4-cycle counting and all-pairs-shortest-paths. ...
As described earlier, our algorithm is fast also in the case where only one of the input matrices is sparse, as stated in the following corollary of Theorem 1. Corollary 4. ...
Then, Le Gall [14] provided fast algorithms for multiplying rectangular matrices and algorithms for computing multiple instances of products of independent matrices. ...
doi:10.1016/j.tcs.2019.11.006
fatcat:pxvorrbw2vdf3kfjnydk74h7me
Page 7 of Mathematical Reviews Vol. , Issue 2002A
[page]
2002
Mathematical Reviews
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, Manuel Bronstein and Thom Mulders, Fast deterministic computation of determinants of dense matrices (197-204 (electronic)); Markus A. ...
and Algebraic Computation. ...
Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices
2012
Proceedings of the National Academy of Sciences of the United States of America
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Such universality, if exhibited by deterministic matrices, could be very important, because certain matrices, based on fast Fourier and fast Hadamard transforms, lead to fast and practical iterative reconstruction ...
The deterministic matrices that we study include many associated with fast algorithms, and therefore, our results can be of real practical significance. ...
We would like to thank Michael Saunders and Michael Friedlander for providing us with a prerelease version of the optimization software ASP. ...
doi:10.1073/pnas.1219540110
pmid:23277588
pmcid:PMC3557083
fatcat:7y74q6yoxvfgfiflud52drpmwe
Parallel Hybrid Monte Carlo Algorithms for Matrix Computations
[chapter]
2005
Lecture Notes in Computer Science
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In this paper we consider hybrid (fast stochastic approximation and deterministic refinement) algorithms for Matrix Inversion (MI) and Solving Systems of Linear Equations (SLAE). ...
We show how the stochastic approximation of the MI can be combined with a deterministic refinement procedure to obtain MI with the required precision and further solve the SLAE using MI. ...
Further experiments are required to determine the optimal number of chains required for Monte Carlo procedures and how best to tailor together Monte Carlo and deterministic refinement procedures. if A, ...
doi:10.1007/11428862_102
fatcat:2pjxpwcaifddnpfk4nty66gt6m
Page 1273 of Mathematical Reviews Vol. , Issue 2002B
[page]
2002
Mathematical Reviews
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of determinants of dense matrices. ...
Summary: “In this paper we consider deterministic computation of the exact determinant of a dense matrix M of integers. ...
Efficient matrix rank computation with application to the study of strongly regular graphs
2007
Proceedings of the 2007 international symposium on Symbolic and algebraic computation - ISSAC '07
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We present algorithms for computing the p-rank of integer matrices. ...
The projection is extremely sparse, is chosen according to one of several heuristics, and is combined with a small dense certifying component. ...
Algorithm 1: Rank of matrix A ∈ GF (p) n×n , computed deterministically. Step 1: Determine b such that b rows of A may be stored in main memory. ...
doi:10.1145/1277548.1277586
dblp:conf/issac/MaySW07
fatcat:izx5bgp2mrctvople4c73cdggy
Stochastic parameterization with VARX processes
[article]
2020
arXiv
pre-print
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To reduce the number of parameters of the VARX we impose a diagonal structure on its coefficient matrices. ...
We also show that the parameterization performs accurately for the very challenging trimodal L96 configuration by allowing for a dense (non-diagonal) VARX covariance matrix. ...
In the alternate case of fully dense covariance, the matrix root ΣL is computed with a Cholesky decomposition. ...
arXiv:2010.03293v1
fatcat:uiu3eabz7raxtjuyiyq5c3saau
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