UMFPACK swMATH ID: 989 Software Authors: Davis, Timothy A. Description: 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.The 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. Homepage: http://www.cise.ufl.edu/research/sparse/umfpack/ Dependencies: Matlab Keywords: sparse LU factorization; column pre-ordering strategy; right-looking unsymmetric-pattern multifrontal numerical factorization; UMFPACK Related Software: FreeFem++; PETSc; deal.ii; MUMPS; Trilinos; Matlab; LAPACK; SuperLU; Gmsh; ARPACK; SparseMatrix; PARDISO; CHOLMOD; ALBERTA; FEniCS; CSparse; MooNMD; DUNE; SLEPc; HSL Cited in: 428 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Algorithm 832: UMFPACK V4.3 – an unsymmetric-pattern multifrontal method. Zbl 1072.65037Davis, Timothy A. 2004 all top 5 Cited by 862 Authors 20 Oyarzúa, Ricardo 16 John, Volker 15 Gatica, Gabriel N. 14 Nürnberg, Robert 13 Garcke, Harald 10 Caucao, Sergio 9 Bangerth, Wolfgang 8 Davis, Timothy Alden 8 Heltai, Luca 8 Pelteret, Jean-Paul 7 Heister, Timo 7 Kronbichler, Martin 7 Maier, Matthias Sebastian 7 Turcksin, Bruno 6 Adler, James H. 6 Arndt, Daniel 6 Langer, Ulrich 6 MacLachlan, Scott P. 6 Stoll, Martin 6 Zepeda-Núñez, Leonardo 5 Barrett, John William 5 Colmenares, Eligio 5 di Serafino, Daniela 5 Filippone, Salvatore 5 Flemisch, Bernd 5 Gläser, Dennis 5 Horáček, Jaromir 5 Novo, Julia 5 Scheichl, Robert 5 Sváček, Petr 5 Voigt, Axel 4 Aland, Sebastian 4 Bochev, M. A. 4 D’Ambra, Pasqua 4 Davydov, Denis 4 Demanet, Laurent 4 Endtmayer, Bernhard 4 Fehling, Marc 4 Helmig, Rainer 4 Hu, Xiaozhe 4 Kahle, Christian 4 Schneider, Martin 4 Solano, Manuel E. 4 Weishaupt, Kilian 4 Wick, Thomas 4 Yue, Pengtao 4 Zhang, Jiaqi 4 Zúñiga, Paulo 3 Achdou, Yves 3 Bollhöfer, Matthias 3 Bosch, Jessica 3 Buttari, Alfredo 3 Camaño, Jessika 3 Carraro, Thomas 3 Dastour, Hatef 3 Dedner, Andreas S. 3 Dodwell, Tim J. 3 Eyi, Sinan 3 Feistauer, Miloslav 3 Gassmöller, Rene 3 Hinze, Michael 3 Liao, Wenyuan 3 Lowengrub, John Samuel 3 Manimaran, Jeyaraj 3 Matthies, Gunar 3 Munch, Peter 3 Nakazawa, Takashi 3 Qiu, Hailong 3 Rang, Joachim 3 Sameh, Ahmed H. 3 Shangerganesh, Lingeshwaran 3 Toledo, Sivan 3 Yotov, Ivan 3 Zhao, Hongkai 2 Ahmed, Sarfraz 2 Al-Malki, Faisal A. 2 Allmaras, Steven R. 2 Amestoy, Patrick R. 2 Azegami, Hideyuki 2 Bartels, Sören 2 Bartlett, Roscoe A. 2 Bauer, Georg 2 Benavides, Gonzalo A. 2 Blais, Bruno 2 Blank, Luise 2 Bonito, Andrea 2 Bui-Thanh, Tan 2 Bukshtynov, Vladislav 2 Caiazzo, Alfonso 2 Calo, Victor Manuel 2 Cimrman, Robert 2 Class, Holger 2 Clevenger, Thomas C. 2 Coltman, Edward 2 Dalcín, Lisandro D. 2 Darmofal, David L. 2 Discacciati, Marco 2 Dorfler, Willy 2 Dubcová, Lenka 2 Elliott, Charles M. ...and 762 more Authors all top 5 Cited in 104 Serials 44 Journal of Computational Physics 43 Computer Methods in Applied Mechanics and Engineering 35 SIAM Journal on Scientific Computing 23 Computers & Mathematics with Applications 22 Journal of Computational and Applied Mathematics 16 ACM Transactions on Mathematical Software 14 Journal of Scientific Computing 10 Applied Numerical Mathematics 10 Journal of Numerical Mathematics 9 International Journal for Numerical Methods in Engineering 7 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 6 Journal of Fluid Mechanics 6 Numerische Mathematik 6 Computational Mechanics 6 Computational Geosciences 5 Computers and Fluids 5 Mathematics and Computers in Simulation 5 Numerical Algorithms 4 Calcolo 4 SIAM Journal on Matrix Analysis and Applications 4 Computational Optimization and Applications 4 Numerical Linear Algebra with Applications 4 Mathematical Programming Computation 3 Mathematics of Computation 3 Computing 3 SIAM Journal on Numerical Analysis 3 ETNA. 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