Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization. SuiteSparseQR is a sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method to obtain high performance on multicore architectures. Parallelism across different frontal matrices is handled with Intel’s Threading Building Blocks library. The symbolic analysis and ordering phase pre-eliminates singletons by permuting the input matrix A into the form [R11 R12; 0 A22] where R11 is upper triangular with diagonal entries above a given tolerance. Next, the fill-reducing ordering, column elimination tree, and frontal matrix structures are found without requiring the formation of the pattern of ATA. Approximate rank-detection is performed within each frontal matrix using Heath’s method. While Heath’s method is not always exact, it has the advantage of not requiring column pivoting and thus does not interfere with the fill-reducing ordering. For sufficiently large problems, the resulting sparse QR factorization obtains a substantial fraction of the theoretical peak performance of a multicore computer.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 45 articles )

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  1. Al Daas, Hussam; Jolivet, Pierre; Scott, Jennifer A.: A robust algebraic domain decomposition preconditioner for sparse normal equations (2022)
  2. Brenner, Holger; Steinbuch, Jonathan: Deciding stability of sheaves on curves (2022)
  3. Brust, Johannes J.; Marcia, Roummel F.; Petra, Cosmin G.; Saunders, Michael A.: Large-scale optimization with linear equality constraints using reduced compact representation (2022)
  4. Gnanasekaran, Abeynaya; Darve, Eric: Hierarchical orthogonal factorization: sparse square matrices (2022)
  5. Hanke, Michael; März, Roswitha: Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations. I: Basics and ansatz function choices (2022)
  6. Hanke, Michael; März, Roswitha: Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations. II: The discrete least-squares problem (2022)
  7. Jiao, Xiangmin; Chen, Qiao: Approximate generalized inverses with iterative refinement for (\epsilon)-accurate preconditioning of singular systems (2022)
  8. Jorge Barrasa-Fano, Apeksha Shapeti, Álvaro Jorge-Peñas, Mojtaba Barzegari, José Antonio Sanz-Herrera, Hans Van Oosterwyck: TFMLAB: A MATLAB toolbox for 4D traction force microscopy (2021) not zbMATH
  9. Ploskas, Nikolaos; Sahinidis, Nikolaos V.; Samaras, Nikolaos: A triangulation and fill-reducing initialization procedure for the simplex algorithm (2021)
  10. Sobczyk, Aleksandros; Gallopoulos, Efstratios: Estimating leverage scores via rank revealing methods and randomization (2021)
  11. Vanderstukken, Jeroen; De Lathauwer, Lieven: Systems of polynomial equations, higher-order tensor decompositions, and multidimensional harmonic retrieval: a unifying framework. Part I: the canonical polyadic decomposition (2021)
  12. Agnese, Marco; Nürnberg, Robert: Fitted front tracking methods for two-phase ncompressible Navier-Stokes flow: Eulerian and ALE finite element discretizations (2020)
  13. Buttari, Alfredo; Hauberg, Søren; Kodsi, Costy: Parallel \textitQRfactorization of block-tridiagonal matrices (2020)
  14. Lundquist, Tomas; Malan, Arnaud G.; Nordström, Jan: Efficient and error minimized coupling procedures for unstructured and moving meshes (2020)
  15. Müller, Jens-Dominik; Zhang, Xingchen; Akbarzadeh, Siamak; Wang, Yang: Geometric continuity constraints of automatically derived parametrisations in CAD-based shape optimisation (2019)
  16. Roininen, Lassi; Girolami, Mark; Lasanen, Sari; Markkanen, Markku: Hyperpriors for Matérn fields with applications in Bayesian inversion (2019)
  17. Druinsky, Alex; Carlebach, Eyal; Toledo, Sivan: Wilkinson’s inertia-revealing factorization and its application to sparse matrices. (2018)
  18. Essid, Montacer; Solomon, Justin: Quadratically regularized optimal transport on graphs (2018)
  19. 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)
  20. Gould, Nicholas; Scott, Jennifer: The state-of-the-art of preconditioners for sparse linear least-squares problems (2017)

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