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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

doi:10.3837/tiis.2017.05.009
fatcat:z3xatzs3wbfs3p5cdxenvuoauu
*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] . ...##
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Efficient computation of the characteristic polynomial

2005
*
Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05
*

We deal with the

doi:10.1145/1073884.1073905
dblp:conf/issac/DumasPW05
fatcat:pswfsqhp3rcqzn6sr5q6jsfnri
*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 ...##
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An Adaptable Fast Matrix Multiplication Algorithm, Going Beyond the Myth of Decimal War
[article]

2013
*
arXiv
*
pre-print

In this paper we present an adaptable

arXiv:1308.2400v1
fatcat:z6e562jwfve6jbptol5hmvttja
*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*. ...##
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Efficient Computation of the Characteristic Polynomial
[article]

2005
*
arXiv
*
pre-print

This article deals with the

arXiv:cs/0501074v2
fatcat:lgyughj5ujhw3lxljtcvxikhlm
*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*. ...##
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Deterministic CUR for Improved Large-Scale Data Analysis: An Empirical Study
[chapter]

2012
*
Proceedings of the 2012 SIAM International Conference on Data Mining
*

However, these are hardly applicable to large

doi:10.1137/1.9781611972825.59
dblp:conf/sdm/ThurauKB12
fatcat:3gocf3m5q5dnxfqjtocd7pbuwi
*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*. ...##
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Mixed Monte Carlo Parallel Algorithms for Matrix Computation
[chapter]

2002
*
Lecture Notes in Computer Science
*

Experimental results with

doi:10.1007/3-540-46080-2_63
fatcat:rlgjbzqxijct7fzw4dkbslliwq
*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. ...##
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Sparse Matrix Multiplication and Triangle Listing in the Congested Clique Model
[article]

2019
*
arXiv
*
pre-print

Moreover, this new

arXiv:1802.04789v4
fatcat:tmvmycoeorh3lckwtzeybki4fu
*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*. ...##
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Monte Carlo linear solvers with non-diagonal splitting

2010
*
Mathematics and Computers in Simulation
*

The significance

doi:10.1016/j.matcom.2009.03.010
fatcat:73yy4pzawvberc3f6syjhtqezu
*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. ...##
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Sparse matrix multiplication and triangle listing in the Congested Clique model

2019
*
Theoretical Computer Science
*

As applications, we show how to speed up the

doi:10.1016/j.tcs.2019.11.006
fatcat:pxvorrbw2vdf3kfjnydk74h7me
*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*. ...##
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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*. ...##
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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
*

Such universality, if exhibited by

doi:10.1073/pnas.1219540110
pmid:23277588
pmcid:PMC3557083
fatcat:7y74q6yoxvfgfiflud52drpmwe
*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. ...##
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Parallel Hybrid Monte Carlo Algorithms for Matrix Computations
[chapter]

2005
*
Lecture Notes in Computer Science
*

In this paper we consider hybrid (

doi:10.1007/11428862_102
fatcat:2pjxpwcaifddnpfk4nty66gt6m
*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, ...##
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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. ...

##
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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
*

We present algorithms for

doi:10.1145/1277548.1277586
dblp:conf/issac/MaySW07
fatcat:izx5bgp2mrctvople4c73cdggy
*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. ...##
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Stochastic parameterization with VARX processes
[article]

2020
*
arXiv
*
pre-print

To reduce the number

arXiv:2010.03293v1
fatcat:uiu3eabz7raxtjuyiyq5c3saau
*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. ...
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