The university of Florida sparse matrix collection

We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications. The Collection is widely used by the numerical linear algebra community for the development and performance evaluation of sparse matrix algorithms. It allows for robust and repeatable experiments: robust because performance results with artificially generated matrices can be misleading, and repeatable because matrices are curated and made publicly available in many formats. Its matrices cover a wide spectrum of domains, include those arising from problems with underlying 2D or 3D geometry (as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, power networks, and other networks and graphs). We provide software for accessing and managing the Collection, from MATLAB#8482;, Mathematica#8482;, Fortran, and C, as well as an online search capability. Graph visualization of the matrices is provided, and a new multilevel coarsening scheme is proposed to facilitate this task.

[1]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[2]  C. Mudie.  Navigating the ‘Small World’ , 1959 .

[3]  N. S. Mendelsohn,et al.  Two Algorithms for Bipartite Graphs , 1963 .

[4]  R. Willoughby,et al.  Some results on sparse matrices , 1970 .

[5]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[6]  I. Duff.  A survey of sparse matrix research , 1977, Proceedings of the IEEE.

[7]  Iain S. Duff,et al.  On Algorithms for Obtaining a Maximum Transversal , 1981, TOMS.

[8]  Alan George,et al.  Computer Solution of Large Sparse Positive Definite , 1981 .

[9]  John G. Lewis,et al.  Sparse matrix test problems , 1982, SGNM.

[10]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[11]  A. George,et al.  A Comparison of Some Methods for Solving Sparse Linear Least-Squares Problems , 1983 .

[12]  W. Miller.  The engineering of numerical software , 1984 .

[13]  J. Gilbert,et al.  Sparse Partial Pivoting in Time Proportional to Arithmetic Operations , 1986 .

[14]  K. D. Ikramov.  Sparse matrices , 2020, Krylov Subspace Methods with Application in Incompressible Fluid Flow Solvers.

[15]  Piet Hut,et al.  A hierarchical O(N log N) force-calculation algorithm , 1986, Nature.

[16]  Ed Anderson,et al.  LAPACK Users' Guide , 1995 .

[17]  A. Edelman.  Eigenvalues and condition numbers of random matrices , 1988 .

[18]  V. Rich.  Personal communication , 1989, Nature.

[19]  Alex Pothen,et al.  Computing the block triangular form of a sparse matrix , 1990, TOMS.

[20]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[21]  Z. Zlatev.  Computational Methods for General Sparse Matrices , 1991 .

[22]  Timothy A. Davis,et al.  An Unsymmetric-pattern Multifrontal Method for Sparse Lu Factorization , 1993 .

[23]  J. Mulvey,et al.  SOLVING MULTISTAGE STOCHASTIC PROGRAMS WITH TREE DISSECTION , 1991 .

[24]  Barry W. Peyton,et al.  Block sparse Cholesky algorithms on advanced uniprocessor computers , 1991 .

[25]  Edward M. Reingold,et al.  Graph drawing by force‐directed placement , 1991, Softw. Pract. Exp..

[26]  Stephen E. Zitney,et al.  Sparse matrix methods for chemical process separation calculations on supercomputers , 1992, Proceedings Supercomputing '92.

[27]  John R. Gilbert,et al.  Sparse Matrices in MATLAB: Design and Implementation , 1992, SIAM J. Matrix Anal. Appl..

[28]  Zvi Drezner,et al.  Computing Lower Bounds for the Quadratic Assignment Problem with an Interior Point Algorithm for Linear Programming , 1995, Oper. Res..

[29]  David E. Long,et al.  Efficient frequency domain analysis of large nonlinear analog circuits , 1996, Proceedings of Custom Integrated Circuits Conference.

[30]  Patrick R. Amestoy,et al.  An Approximate Minimum Degree Ordering Algorithm , 1996, SIAM J. Matrix Anal. Appl..

[31]  Richard F. Barrett,et al.  Matrix Market: a web resource for test matrix collections , 1996, Quality of Numerical Software.

[32]  John K. Reid,et al.  Exploiting zeros on the diagonal in the direct solution of indefinite sparse symmetric linear systems , 1996, TOMS.

[33]  Anshul Gupta,et al.  Fast and effective algorithms for graph partitioning and sparse-matrix ordering , 1997, IBM J. Res. Dev..

[34]  Iain S. Duff,et al.  The Rutherford-Boeing sparse matrix collection , 1997 .

[35]  I. Duff,et al.  The state of the art in numerical analysis , 1997 .

[36]  Michele Benzi,et al.  A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems , 1998, SIAM J. Sci. Comput..

[37]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[38]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[39]  James Demmel,et al.  An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination , 1997, SIAM J. Matrix Anal. Appl..

[40]  James Demmel,et al.  A Supernodal Approach to Sparse Partial Pivoting , 1999, SIAM J. Matrix Anal. Appl..

[41]  Jeremy P. Spinrad,et al.  Modular decomposition and transitive orientation , 1999, Discret. Math..

[42]  Iain S. Duff,et al.  The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices , 1999, SIAM J. Matrix Anal. Appl..

[43]  Jack Dongarra,et al.  LAPACK Users' Guide, 3rd ed. , 1999 .

[44]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[45]  Rajeev Motwani,et al.  The PageRank Citation Ranking : Bringing Order to the Web , 1999, WWW 1999.

[46]  Timothy A. Davis,et al.  A combined unifrontal/multifrontal method for unsymmetric sparse matrices , 1999, TOMS.

[47]  H. V. D. Vorst,et al.  A parallel linear system solver for circuit simulation problems , 2000 .

[48]  Chris Walshaw,et al.  Journal of Graph Algorithms and Applications a Multilevel Algorithm for Force-directed Graph-drawing , 2022 .

[49]  James Demmel,et al.  Non-Hermitian Eigenvalue Problems , 2000, Templates for the Solution of Algebraic Eigenvalue Problems.

[50]  Hossein Sedarat,et al.  On the optimality of the gridding reconstruction algorithm , 2000, IEEE Transactions on Medical Imaging.

[51]  Henk A. van der Vorst,et al.  A parallel linear system solver for circuit simulation problems , 2000, Numer. Linear Algebra Appl..

[52]  Patrick Amestoy,et al.  A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling , 2001, SIAM J. Matrix Anal. Appl..

[53]  Sivan Toledo,et al.  Nested-Dissection Orderings for Sparse LU with Partial Pivoting , 2000, SIAM J. Matrix Anal. Appl..

[54]  R. Bisseling,et al.  DNA Electrophoresis Studied with the Cage Model , 2001, cond-mat/0101467.

[55]  Jürgen Schulze.  Towards a Tighter Coupling of Bottom-Up and Top-Down Sparse Matrix Ordering Methods , 2001 .

[56]  Arnold Reusken,et al.  Approximation of the Determinant of Large Sparse Symmetric Positive Definite Matrices , 2000, SIAM J. Matrix Anal. Appl..

[57]  Patrick Amestoy,et al.  An Unsymmetrized Multifrontal LU Factorization , 2000, SIAM J. Matrix Anal. Appl..

[58]  N. Trefethen.  A Hundred-dollar Hundred-digit Challenge , 2002 .

[59]  Anshul Gupta,et al.  Improved Symbolic and Numerical Factorization Algorithms for Unsymmetric Sparse Matrices , 2002, SIAM J. Matrix Anal. Appl..

[60]  Eric R. Keiter,et al.  Computational Algorithms for Device-Circuit Coupling , 2003 .

[61]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[62]  A Multilevel Algorithm for Force-Directed Graph-Drawing , 2003, J. Graph Algorithms Appl..

[63]  E.,et al.  MULTIFRONTAL VS FRONTAL TECHNIQUES FOR ‘ i .-CHEMICAL PROCESS SIMULATION ON , . SUPERCOMPUTERS , 2003 .

[64]  Timothy A. Davis,et al.  Algorithm 837: AMD, an approximate minimum degree ordering algorithm , 2004, TOMS.

[65]  Michael Jünger,et al.  Drawing Large Graphs with a Potential-Field-Based Multilevel Algorithm , 2004, GD.

[66]  Timothy A. Davis,et al.  A column approximate minimum degree ordering algorithm , 2000, TOMS.

[67]  Timothy A. Davis,et al.  A column pre-ordering strategy for the unsymmetric-pattern multifrontal method , 2004, TOMS.

[68]  Taher H. Haveliwala,et al.  Adaptive methods for the computation of PageRank , 2004 .

[69]  Iain S. Duff,et al.  Strategies for Scaling and Pivoting for Sparse Symmetric Indefinite Problems , 2005, SIAM J. Matrix Anal. Appl..

[70]  Christos Faloutsos,et al.  Realistic, Mathematically Tractable Graph Generation and Evolution, Using Kronecker Multiplication , 2005, PKDD.

[71]  Timothy A. Davis,et al.  Algorithm 8 xx : a concise sparse Cholesky factorization package , 2004 .

[72]  Ira Kemelmacher-Shlizerman,et al.  Indexing with unknown illumination and pose , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[73]  Iain S. Duff.  Pivot selection and row ordering in givens reduction on sparse matrices , 2005, Computing.

[74]  B. RudnyiE.,et al.  Model Reduction for High Dimensional Micro-FE Models , 2006 .

[75]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[76]  Xiaoye S. Li,et al.  Diagonal Markowitz Scheme with Local Symmetrization , 2003, SIAM J. Matrix Anal. Appl..

[77]  Yifan Hu,et al.  Efficient, High-Quality Force-Directed Graph Drawing , 2006 .

[78]  YANQING CHEN,et al.  Algorithm 8 xx : CHOLMOD , supernodal sparse Cholesky factorization and update / downdate ∗ , 2006 .

[79]  Timothy A. Davis,et al.  Dynamic Supernodes in Sparse Cholesky Update/Downdate and Triangular Solves , 2009, TOMS.

[80]  Desmond J. Higham,et al.  CONTEST: A Controllable Test Matrix Toolbox for MATLAB , 2009, TOMS.