UMFPACK

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: http://dl.acm.org/)


References in zbMATH (referenced in 325 articles , 1 standard article )

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  1. 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)
  2. Endtmayer, B.; Langer, U.; Wick, T.: Two-side a posteriori error estimates for the dual-weighted residual method (2020)
  3. Failer, L.; Richter, T.: A parallel Newton multigrid framework for monolithic fluid-structure interactions (2020)
  4. Farrell, Patrick E.; Gazca-Orozco, P. A.; Süli, Endre: Numerical analysis of unsteady implicitly constituted incompressible fluids: 3-field formulation (2020)
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  8. Abdulla, Ugur G.; Bukshtynov, Vladislav; Hagverdiyev, Ali: Gradient method in Hilbert-Besov spaces for the optimal control of parabolic free boundary problems (2019)
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  10. Arndt, Daniel; Bangerth, Wolfgang; Clevenger, Thomas C.; Davydov, Denis; Fehling, Marc; Garcia-Sanchez, Daniel; Harper, Graham; Heister, Timo; Heltai, Luca; Kronbichler, Martin; Kynch, Ross Maguire; Maier, Matthias; Pelteret, Jean-Paul; Turcksin, Bruno; Wells, David: The deal.II library, Version 9.1 (2019)
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  17. Endtmayer, Bernhard; Langer, Ulrich; Wick, Thomas: Multigoal-oriented error estimates for non-linear problems (2019)
  18. 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)
  19. Giannetti, F.; Camarri, S.; Citro, V.: Sensitivity analysis and passive control of the secondary instability in the wake of a cylinder (2019)
  20. Gläser, Dennis; Flemisch, Bernd; Helmig, Rainer; Class, Holger: A hybrid-dimensional discrete fracture model for non-isothermal two-phase flow in fractured porous media (2019)

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