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Semi-deterministic Sparse Matrix for Low Complexity Compressive Sampling

2017 KSII Transactions on Internet and Information Systems  
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

Jean-Guillaume Dumas, Clément Pernet, Zhendong Wan
2005 Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05  
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]

Niraj Kumar Singh, Soubhik Chakraborty, Dheeresh Kumar Mallick
2013 arXiv   pre-print
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]

Jean-Guillaume Dumas , Zhendong Wan
2005 arXiv   pre-print
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]

Christian Thurau, Kristian Kersting, Christian Bauckhage
2012 Proceedings of the 2012 SIAM International Conference on Data Mining  
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]

Behrouz Fathi, Bo Liu, Vassil Alexandrov
2002 Lecture Notes in Computer Science  
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]

Keren Censor-Hillel, Dean Leitersdorf, Elia Turner
2019 arXiv   pre-print
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

A. Srinivasan
2010 Mathematics and Computers in Simulation  
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

Keren Censor-Hillel, Dean Leitersdorf, Elia Turner
2019 Theoretical Computer Science  
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  
, 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

Hatef Monajemi, Sina Jafarpour, Matan Gavish, David L. Donoho
2012 Proceedings of the National Academy of Sciences of the United States of America  
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]

V. Alexandrov, E. Atanassov, I. Dimov, S. Branford, A. Thandavan, C. Weihrauch
2005 Lecture Notes in Computer Science  
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  
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

John P. May, David Saunders, Zhendong Wan
2007 Proceedings of the 2007 international symposium on Symbolic and algebraic computation - ISSAC '07  
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]

Nick Verheul, Daan Crommelin
2020 arXiv   pre-print
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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