Matrix Market: a web resource for test matrix collections

Boisvert, Ronald F.; Pozo, Roldan; Remington, Karin; Barrett, Richard Frederick; Dongarra, Jack

doi:10.1007/978-1-5041-2940-4_9

Cited by 199 publications

(170 citation statements)

References 2 publications

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“…The results are summarized in Table 3. Matrices can-xx and bcspwr03 are from the library Matrix Market [41], grid3dt matrices are 3D cubical meshes, gridt matrices are 2D triangular meshes, and Smallmesh is a 2D finite-element mesh. Lower bounds for the min-cut problem presented in the table are obtained by approximately solving S D P 4 , i.e., by iteratively adding the most violated inequalities of type (16)- (19) and (20) to S D P 2 .…”

Section: Computational Resultsmentioning

confidence: 99%

The min-cut and vertex separator problem

Rendl¹,

Sotirov

2017

Comput Optim Appl

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We consider graph three-partitions with the objective of minimizing the number of edges between the first two partition sets while keeping the size of the third block small. We review most of the existing relaxations for this min-cut problem and focus on a new class of semidefinite relaxations, based on matrices of order 2n + 1 which provide a good compromise between quality of the bound and computational effort to actually compute it. Here, n is the order of the graph. Our numerical results indicate that the new bounds are quite strong and can be computed for graphs of medium size (n ≈ 300) with reasonable effort of a few minutes of computation time. Further, we exploit those bounds to obtain bounds on the size of the vertex separators. A vertex separator is a subset of the vertex set of a graph whose removal splits the graph into two disconnected subsets. We also present an elegant way of convexifying nonconvex quadratic problems by using semidefinite programming. This approach results with bounds that can be computed with any standard convex quadratic programming solver.

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Section: Computational Resultsmentioning

confidence: 99%

The min-cut and vertex separator problem

Rendl¹,

Sotirov

2017

Comput Optim Appl

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“…Matrix Depot provides access to matrices from Matrix Market (Boisvert et al, 1997) and the University of Florida Sparse Matrix Collection (Davis & Hu, 2011), both of which contain many matrices taken from applications. In particular, these sources contain many large, sparse matrices.…”

Section: Matrix Data From External Sourcesmentioning

confidence: 99%

Matrix Depot: an extensible test matrix collection for Julia

Zhang

Higham

2016

PeerJ Computer Science

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Matrix Depot is a Julia software package that provides easy access to a large and diverse collection of test matrices. Its novelty is threefold. First, it is extensible by the user, and so can be adapted to include the user's own test problems. In doing so, it facilitates experimentation and makes it easier to carry out reproducible research. Second, it amalgamates in a single framework two different types of existing matrix collections, comprising parametrized test matrices (including Hansen's set of regularization test problems and Higham's Test Matrix Toolbox) and real-life sparse matrix data (giving access to the University of Florida sparse matrix collection). Third, it fully exploits the Julia language. It uses multiple dispatch to help provide a simple interface and, in particular, to allow matrices to be generated in any of the numeric data types supported by the language.

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“…In this section, we test the efficiency of the proposed algorithms for the model updating problem in structural engineering, where the mass and stiffness matrix M and K are obtained from the set BCSSTRUC1 in the Harwell-Boeing Collection [3] and the damping matrix C are Rayleigh damping [8,10]:…”

Section: A Model Updating Problem In Structural Engineeringmentioning

confidence: 99%