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, Mathematica, 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.

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  1. Benner, Peter; Bujanović, Zvonimir; Kürschner, Patrick; Saak, Jens: RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations (2018)
  2. Fasi, Massimiliano; Iannazzo, Bruno: Computing the weighted geometric mean of two large-scale matrices and its inverse times a vector (2018)
  3. Grigori, Laura; Cayrols, Sebastien; Demmel, James W.: Low rank approximation of a sparse matrix based on LU factorization with column and row tournament pivoting (2018)
  4. Gu, Xian-Ming; Huang, Ting-Zhu; Yin, Guojian; Carpentieri, Bruno; Wen, Chun; Du, Lei: Restarted Hessenberg method for solving shifted nonsymmetric linear systems (2018)
  5. Hager, William W.; Hungerford, James T.; Safro, Ilya: A multilevel bilinear programming algorithm for the vertex separator problem (2018)
  6. Schlüter, Federico; Strappa, Yanela; Milone, Diego H.; Bromberg, Facundo: Blankets joint posterior score for learning Markov network structures (2018)
  7. Shojaei-Fard, Alireza; Amroudi, Ali Nakhaei: An efficient method for solving a quaternionic least-squares problem (2018)
  8. Yang, Wangdong; Li, Kenli; Li, Keqin: A parallel computing method using blocked format with optimal partitioning for SpMV on GPU (2018)
  9. Zhang, Lei-Hong; Shen, Chungen; Yang, Wei Hong; Júdice, Joaquim J.: A Lanczos method for large-scale extreme Lorentz eigenvalue problems (2018)
  10. Ahmadi-Asl, Salman; Beik, Fatemeh Panjeh Ali: Iterative algorithms for least-squares solutions of a quaternion matrix equation (2017)
  11. Aihara, Kensuke: Variants of the groupwise update strategy for short-recurrence Krylov subspace methods (2017)
  12. Bakhos, Tania; Kitanidis, Peter K.; Ladenheim, Scott; Saibaba, Arvind K.; Szyld, Daniel B.: Multipreconditioned gmres for shifted systems (2017)
  13. Bentbib, Abdeslem Hafid; Jbilou, Khalide; Sadek, El Mostafa: On some extended block Krylov based methods for large scale nonsymmetric Stein matrix equations (2017)
  14. Benzi, Michele; Uçar, Bora: Preconditioning techniques based on the Birkhoff-von Neumann decomposition (2017)
  15. Berljafa, Mario; Güttel, Stefan: Parallelization of the rational Arnoldi algorithm (2017)
  16. Boutsidis, Christos; Drineas, Petros; Kambadur, Prabhanjan; Kontopoulou, Eugenia-Maria; Zouzias, Anastasios: A randomized algorithm for approximating the log determinant of a symmetric positive definite matrix (2017)
  17. Carson, Erin; Higham, Nicholas J.: A new analysis of iterative refinement and its application to accurate solution of ill-conditioned sparse linear systems (2017)
  18. Cerdán, J.; Marín, J.; Mas, J.: Low-rank updates of balanced incomplete factorization preconditioners (2017)
  19. Eisenstat, Stanley C.; Gratton, Serge; Titley-Peloquin, David: On the symmetric componentwise relative backward error for linear systems of equations (2017)
  20. Fika, Paraskevi; Mitrouli, Marilena: Aitken’s method for estimating bilinear forms arising in applications (2017)

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