An ANSI C code for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The pre-ordering and symbolic analysis phase computes an upper bound on fill-in, work, and memory usage during the subsequent numerical factorization. User-callable routines are provided for ordering and analyzing a sparse matrix, computing the numerical factorization, solving a system with the LU factors, transposing and permuting a sparse matrix, and converting between sparse matrix representations.\parThe simple user interface shields the user from the details of the complex sparse factorization data structures by returning simple handles to opaque objects. Additional user-callable routines are provided for printing and extracting the contents of these opaque objects. An even simpler way to use the package is through its MATLAB interface. UMFPACK is incorporated as a built-in operator in MATLAB 6.5 as $x= A^{-1} {\bold b}$ when $A$ is sparse and unsymmetric. (Source:

References in zbMATH (referenced in 274 articles , 1 standard article )

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  1. Abdulla, Ugur G.; Bukshtynov, Vladislav; Hagverdiyev, Ali: Gradient method in Hilbert-Besov spaces for the optimal control of parabolic free boundary problems (2019)
  2. Detommaso, Gianluca; Dodwell, Tim; Scheichl, Rob: Continuous level Monte Carlo and sample-adaptive model hierarchies (2019)
  3. Gander, Martin J.; Zhang, Hui: A class of iterative solvers for the Helmholtz equation: factorizations, sweeping preconditioners, source transfer, single layer potentials, polarized traces, and optimized Schwarz methods (2019)
  4. Giannetti, F.; Camarri, S.; Citro, V.: Sensitivity analysis and passive control of the secondary instability in the wake of a cylinder (2019)
  5. Hook, James; Pestana, Jennifer; Tisseur, Françoise; Hogg, Jonathan: Max-balanced Hungarian scalings (2019)
  6. 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)
  7. Kou, Jisheng; Sun, Shuyu; Wu, Yuanqing: A semi-analytic porosity evolution scheme for simulating wormhole propagation with the Darcy-Brinkman-Forchheimer model (2019)
  8. Rabault, Jean; Kuchta, Miroslav; Jensen, Atle; Réglade, Ulysse; Cerardi, Nicolas: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control (2019)
  9. Zhang, Rui; Wen, Lihua; Xiao, Jinyou; Qian, Dong: An efficient solution algorithm for space-time finite element method (2019)
  10. Almonacid, Javier A.; Gatica, Gabriel N.; Oyarzúa, Ricardo: A mixed-primal finite element method for the Boussinesq problem with temperature-dependent viscosity (2018)
  11. Alzetta, Giovanni; Arndt, Daniel; Bangerth, Wolfgang; Boddu, Vishal; Brands, Benjamin; Davydov, Denis; Gassmöller, Rene; Heister, Timo; Heltai, Luca; Kormann, Katharina; Kronbichler, Martin; Maier, Matthias; Pelteret, Jean-Paul; Turcksin, Bruno; Wells, David: The deal.II library, version 9.0 (2018)
  12. Botchev, M. A.; Hanse, A. M.; Uppu, R.: Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources (2018)
  13. Camaño, Jessika; Muñoz, Cristian; Oyarzúa, Ricardo: Numerical analysis of a dual-mixed problem in non-standard Banach spaces (2018)
  14. Carraro, Thomas; Dörsam, Simon; Frei, Stefan; Schwarz, Daniel: An adaptive Newton algorithm for optimal control problems with application to optimal electrode design (2018)
  15. Caucha, Luis J.; Frei, Stefan; Rubio, Obidio: Finite element simulation of fluid dynamics and CO(_2) gas exchange in the alveolar sacs of the human lung (2018)
  16. Garcke, Harald; Lam, Kei Fong; Nürnberg, Robert; Sitka, Emanuel: A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis (2018)
  17. Gatica, Luis F.; Oyarzúa, Ricardo; Sánchez, Nestor: A priori and a posteriori error analysis of an augmented mixed-FEM for the Navier-Stokes-Brinkman problem (2018)
  18. Jayasinghe, Savithru; Darmofal, David L.; Burgess, Nicholas K.; Galbraith, Marshall C.; Allmaras, Steven R.: A space-time adaptive method for reservoir flows: formulation and one-dimensional application (2018)
  19. Kim, Youngdae; Huber, Olivier; Ferris, Michael C.: A structure-preserving pivotal method for affine variational inequalities (2018)
  20. Nicholson, Bethany L.; Wan, Wei; Kameswaran, Shivakumar; Biegler, Lorenz T.: Parallel cyclic reduction strategies for linear systems that arise in dynamic optimization problems (2018)

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