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 354 articles , 1 standard article )

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  1. Bastian, Peter; Blatt, Markus; Dedner, Andreas; Dreier, Nils-Arne; Engwer, Christian; Fritze, René; Gräser, Carsten; Grüninger, Christoph; Kempf, Dominic; Klöfkorn, Robert; Ohlberger, Mario; Sander, Oliver: The \textscDuneframework: basic concepts and recent developments (2021)
  2. Koch, Timo; Gläser, Dennis; Weishaupt, Kilian; Ackermann, Sina; Beck, Martin; Becker, Beatrix; Burbulla, Samuel; Class, Holger; Coltman, Edward; Emmert, Simon; Fetzer, Thomas; Grüninger, Christoph; Heck, Katharina; Hommel, Johannes; Kurz, Theresa; Lipp, Melanie; Mohammadi, Farid; Scherrer, Samuel; Schneider, Martin; Seitz, Gabriele; Stadler, Leopold; Utz, Martin; Weinhardt, Felix; Flemisch, Bernd: DuMu(^\textx 3) -- an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling (2021)
  3. Manimaran, J.; Shangerganesh, L.; Debbouche, Amar: Finite element error analysis of a time-fractional nonlocal diffusion equation with the Dirichlet energy (2021)
  4. Adler, J. H.; Gaspar, F. J.; Hu, X.; Ohm, P.; Rodrigo, C.; Zikatanov, L. T.: Robust preconditioners for a new stabilized discretization of the poroelastic equations (2020)
  5. Arndt, Daniel; Bangerth, Wolfgang; Blais, Bruno; Clevenger, Thomas C.; Fehling, Marc; Grayver, Alexander V.; Heister, Timo; Heltai, Luca; Kronbichler, Martin; Maier, Matthias; Munch, Peter; Pelteret, Jean-Paul; Rastak, Reza; Tomas, Ignacio; Turcksin, Bruno; Wang, Zhuoran; Wells, David: The deal.II library, version 9.2 (2020)
  6. Colmenares, Eligio; Gatica, Gabriel N.; Moraga, Sebastián: A Banach spaces-based analysis of a new fully-mixed finite element method for the Boussinesq problem (2020)
  7. de Carvalho, Pitágoras P.; Fernández-Cara, Enrique: Numerical Stackelberg-Nash control for the heat equation (2020)
  8. Diwan, Ganesh C.; Mohamed, M. Shadi: Iterative solution of Helmholtz problem with high-order isogeometric analysis and finite element method at mid-range frequencies (2020)
  9. Endtmayer, Bernhard; Langer, Ulrich.; Neitzel, I.; Wick, Thomas; Wollner, W.: Multigoal-oriented optimal control problems with nonlinear PDE constraints (2020)
  10. Endtmayer, B.; Langer, U.; Wick, T.: Two-side a posteriori error estimates for the dual-weighted residual method (2020)
  11. Evgrafov, Anton; Bellido, José C.: Nonlocal control in the conduction coefficients: well-posedness and convergence to the local limit (2020)
  12. Failer, L.; Richter, T.: A parallel Newton multigrid framework for monolithic fluid-structure interactions (2020)
  13. Farrell, Patrick E.; Gazca-Orozco, P. A.; Süli, Endre: Numerical analysis of unsteady implicitly constituted incompressible fluids: 3-field formulation (2020)
  14. Gatica, Gabriel N.; Inzunza, Cristian: An augmented fully-mixed finite element method for a coupled flow-transport problem (2020)
  15. Gatica, Gabriel N.; Oyarzúa, Ricardo; Valenzuela, Nathalie: A five-field augmented fully-mixed finite element method for the Navier-Stokes/Darcy coupled problem (2020)
  16. Hartwig Anzt, Terry Cojean, Yen-Chen Chen, Goran Flegar, Fritz Göbel, Thomas Grützmacher, Pratik Nayak, Tobias Ribizel, Yu-Hsiang Tsai: Ginkgo: A high performance numerical linear algebra library (2020) not zbMATH
  17. Hawkins, Stuart C.: Algorithm 1009: MieSolver -- an object-oriented Mie series software for wave scattering by cylinders (2020)
  18. Jaust, Alexander; Weishaupt, Kilian; Mehl, Miriam; Flemisch, Bernd: Partitioned coupling schemes for free-flow and porous-media applications with sharp interfaces (2020)
  19. Khapaev, M. M.; Kupriyanov, M. Yu.; Bakurskiy, S. V.; Klenov, N. V.; Soloviev, I. I.: Modeling superconductor SFN-structures using the finite element method (2020)
  20. Oyarzúa, Ricardo; Solano, Manuel; Zúñiga, Paulo: A priori and a posteriori error analyses of a high order unfitted mixed-FEM for Stokes flow (2020)

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