CHOLMOD

Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate. CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AAT, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level-3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both C and MATLABTM interfaces. It appears in MATLAB 7.2 as x = A when A is sparse symmetric positive definite, as well as in several other sparse matrix functions. (Source: http://dl.acm.org/)


References in zbMATH (referenced in 76 articles , 1 standard article )

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  1. Bollhöfer, Matthias; Eftekhari, Aryan; Scheidegger, Simon; Schenk, Olaf: Large-scale sparse inverse covariance matrix estimation (2019)
  2. Hardin, Thomas J.: Accelerating coupled finite element-kinetic Monte Carlo models: (200 \times) speedup of shear transformation zone dynamics simulations (2019)
  3. Howse, Alexander J.; de Sterck, Hans; Falgout, Robert D.; MacLachlan, Scott; Schroder, Jacob: Parallel-in-time multigrid with adaptive spatial coarsening for the linear advection and inviscid Burgers equations (2019)
  4. Druinsky, Alex; Carlebach, Eyal; Toledo, Sivan: Wilkinson’s inertia-revealing factorization and its application to sparse matrices. (2018)
  5. Essid, Montacer; Solomon, Justin: Quadratically regularized optimal transport on graphs (2018)
  6. Fougner, Christopher; Boyd, Stephen: Parameter selection and preconditioning for a graph form solver (2018)
  7. Krattiger, Dimitri; Hussein, Mahmoud I.: Generalized Bloch mode synthesis for accelerated calculation of elastic band structures (2018)
  8. Nhan, Thái Anh; MacLachlan, Scott; Madden, Niall: Boundary layer preconditioners for finite-element discretizations of singularly perturbed reaction-diffusion problems (2018)
  9. Ruipeng Li, Yuanzhe Xi, Lucas Erlandson, Yousef Saad: The Eigenvalues Slicing Library (EVSL): Algorithms, Implementation, and Software (2018) arXiv
  10. Sushnikova, Daria A.; Oseledets, Ivan V.: “Compress and eliminate” solver for symmetric positive definite sparse matrices (2018)
  11. Berkels, Benjamin; Effland, Alexander; Rumpf, Martin: A posteriori error control for the binary Mumford-Shah model (2017)
  12. Gould, Nicholas; Scott, Jennifer: The state-of-the-art of preconditioners for sparse linear least-squares problems (2017)
  13. Russell, Stephen; Madden, Niall: An introduction to the analysis and implementation of sparse grid finite element methods (2017)
  14. Scott, Jennifer: On using Cholesky-based factorizations and regularization for solving rank-deficient sparse linear least-squares problems (2017)
  15. Sencer Nuri Yeralan; Timothy A. Davis; Wissam M. Sid-Lakhdar; Sanjay Ranka: Algorithm 980: Sparse QR Factorization on the GPU (2017) not zbMATH
  16. Bellavia, Stefania; De Simone, Valentina; di Serafino, Daniela; Morini, Benedetta: On the update of constraint preconditioners for regularized KKT systems (2016)
  17. Bouillaguet, Charles; Delaplace, Claire: Sparse Gaussian elimination modulo (p): an update (2016)
  18. Garcke, Harald; Hinze, Michael; Kahle, Christian: A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow (2016)
  19. Genctav, Murat; Genctav, Asli; Tari, Sibel: Nonlocal via local-nonlinear via linear: a new part-coding distance field via screened Poisson equation (2016)
  20. Hager, William W.; Zhang, Hongchao: Projection onto a polyhedron that exploits sparsity (2016)

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