## SuperLU

 swMATH ID: 930 Software Authors: X. Sherry Li; Jim Demmel; John Gilbert; Laura Grigori; Meiyue Shao; Ichitaro Yamazaki Description: SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations on high performance machines. The library is written in C and is callable from either C or Fortran. The library routines will perform an LU decomposition with partial pivoting and triangular system solves through forward and back substitution. The LU factorization routines can handle non-square matrices but the triangular solves are performed only for square matrices. The matrix columns may be preordered (before factorization) either through library or user supplied routines. This preordering for sparsity is completely separate from the factorization. Working precision iterative refinement subroutines are provided for improved backward stability. Routines are also provided to equilibrate the system, estimate the condition number, calculate the relative backward error, and estimate error bounds for the refined solutions. Homepage: http://crd.lbl.gov/~xiaoye/SuperLU/ Keywords: orms Related Software: MUMPS; PETSc; UMFPACK; LAPACK; Trilinos; SuperLU-DIST; PARDISO; METIS; SparseMatrix; HSL; ARPACK; hypre; Matlab; CHOLMOD; BLAS; ScaLAPACK; Gmsh; symrcm; CSparse; WSMP Cited in: 189 Publications This software is also referenced in ORMS.
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### Cited by 469 Authors

 5 Heil, Matthias 4 D’Ambra, Pasqua 3 Demmel, James Weldon 3 Duff, Iain S. 3 Filippone, Salvatore 3 Haslinger, Jaroslav 3 Hazel, Andrew L. 3 Helmig, Rainer 3 Heroux, Michael A. 3 Kees, Christopher E. 3 Mäkinen, Raino A. E. 3 Masson, Roland 3 Pardo, David 3 Paszyński, Maciej 3 Pawlowski, Roger P. 3 Sala, Marzio 3 Shadid, John N. 3 Terekhov, Kirill M. 3 Toivanen, Jukka I. 3 Zlatev, Zahari 2 Al Akhras, H. 2 Amestoy, Patrick R. 2 Apel, Thomas 2 Bollhöfer, Matthias 2 Bompadre, Agustín 2 Čermák, Martin 2 Chen, Pu 2 Cyron, Christian Johannes 2 Davis, Timothy Alden 2 Dawson, Clint N. 2 Demkowicz, Leszek F. 2 Di Pietro, Daniele Antonio 2 Dutra do Carmo, Eduardo Gomes 2 Elguedj, Thomas 2 Farrell, Patrick Emmet 2 Farthing, Matthew W. 2 Flemisch, Bernd 2 Ghosh, Somnath 2 Gilbert, John R. 2 Gravouil, Anthony 2 Grigori, Laura 2 Hapla, Vaclav 2 Hewett, Russell J. 2 Horák, David 2 Jardin, Stephen C. 2 Jolivet, Pierre 2 Ke, Yifen 2 Keeler, Jack S. 2 Kurtz, Jason 2 Lehoucq, Richard B. 2 L’Excellent, Jean-Yves 2 Lin, Paul T. 2 Ma, Changfeng 2 Manguoglu, Murat 2 Mansur, Webe Joao 2 Mihajlović, Milan D. 2 Mitchell, Lawrence 2 Nägel, Arne 2 Negrut, Dan 2 Ortiz, Michael 2 Perotti, Luigi E. 2 Rochette, Michel 2 Salinger, Andrew G. 2 Sameh, Ahmed H. 2 Schenk, Olaf 2 Schneider, Martin 2 Sojka, Radim 2 Stanley, Kendall S. 2 Stebel, Jan 2 Tchelepi, Hamdi A. 2 Trenty, Laurent 2 Tuminaro, Ray S. 2 van de Geijn, Robert Alexander 2 Vassilevski, Panayot Spirov 2 Vassilevski, Yuri V. 2 Wechsung, Florian 2 Wittum, Gabriel 2 Woźniak, Maciej 2 Xia, Jianlin 2 Xu, Xiaowen 2 Yuan, Wei-ran 2 Zepeda-Núñez, Leonardo 2 Zhu, Yao 1 Abril Bucero, Marta 1 Adams, Mark F. 1 Agelas, Leo 1 Aghili, Joubine 1 Agoshkov, Valeriĭ Ivanovich 1 Aguirre-Mesa, Andres M. 1 Ahmad, Mian Ilyas 1 Aizenbud, Yariv 1 Ambikasaran, Sivaram 1 Ammar, Amine 1 Ammon, Martin 1 Ananthan, Shreyas 1 Aprovitola, Andrea 1 Arbenz, Peter 1 Aristizabal, Mauricio 1 Atluri, Satya N. 1 Averbuch, Amir Z. ...and 369 more Authors
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### Cited in 59 Serials

 27 Computer Methods in Applied Mechanics and Engineering 20 Journal of Computational Physics 18 SIAM Journal on Scientific Computing 9 ACM Transactions on Mathematical Software 7 Computers & Mathematics with Applications 6 Journal of Computational and Applied Mathematics 6 Numerical Linear Algebra with Applications 5 Applied Numerical Mathematics 5 Computational Geosciences 4 International Journal for Numerical Methods in Engineering 3 Computers and Fluids 3 Numerische Mathematik 3 Computational Mechanics 2 Journal of Fluid Mechanics 2 Bulletin of Mathematical Biology 2 Mathematics and Computers in Simulation 2 Computer Aided Geometric Design 2 ACM Transactions on Graphics 2 SIAM Journal on Matrix Analysis and Applications 2 Journal of High Energy Physics 1 Inverse Problems 1 Journal of Engineering Mathematics 1 Journal of Mathematical Biology 1 Applied Mathematics and Computation 1 Applied Mathematics and Optimization 1 BIT 1 Calcolo 1 Applied Mathematics and Mechanics. (English Edition) 1 Journal of Computational Mathematics 1 Physica D 1 Journal of Scientific Computing 1 Applications of Mathematics 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 European Journal of Operational Research 1 SIAM Review 1 Applicable Algebra in Engineering, Communication and Computing 1 Archive of Applied Mechanics 1 Journal of Nonlinear Science 1 Mathematica Montisnigri 1 Physics of Fluids 1 Applied and Computational Harmonic Analysis 1 International Journal of Computer Vision 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Engineering Analysis with Boundary Elements 1 Mathematics and Mechanics of Solids 1 Computing and Visualization in Science 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 CMES. Computer Modeling in Engineering & Sciences 1 Computational Methods in Applied Mathematics 1 Journal of Cosmology and Astroparticle Physics 1 Computational Management Science 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Lecture Notes in Computational Science and Engineering 1 Communications in Computational Physics 1 The Journal of Mathematical Neuroscience 1 East Asian Journal on Applied Mathematics 1 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Advances in Applied Mathematics (Boca Raton) 1 SMAI Journal of Computational Mathematics
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### Cited in 31 Fields

 142 Numerical analysis (65-XX) 51 Fluid mechanics (76-XX) 28 Mechanics of deformable solids (74-XX) 23 Partial differential equations (35-XX) 14 Computer science (68-XX) 9 Biology and other natural sciences (92-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Geophysics (86-XX) 6 Optics, electromagnetic theory (78-XX) 6 Operations research, mathematical programming (90-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Statistical mechanics, structure of matter (82-XX) 3 Mechanics of particles and systems (70-XX) 3 Relativity and gravitational theory (83-XX) 3 Systems theory; control (93-XX) 2 Combinatorics (05-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Integral equations (45-XX) 2 Manifolds and cell complexes (57-XX) 2 Statistics (62-XX) 2 Quantum theory (81-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Potential theory (31-XX) 1 Ordinary differential equations (34-XX) 1 Functional analysis (46-XX) 1 Algebraic topology (55-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mathematics education (97-XX)