## ScaLAPACK

 swMATH ID: 830 Software Authors: Blackford, L.S.; Choi, J.; Cleary, A.; D'Azevedo, E.; Demmel, J.; Dhillon, I.; Dongarra, J.; Hammarling, S.; Henry, G.; Petitet, A.; Stanley, K.; Walker, D.; Whaley, R.C. Description: ScaLAPACK is an acronym for scalable linear algebra package or scalable LAPACK. It is a library of high-performance linear algebra routines for distributed memory message-passing MIMD computers and networks of workstations supporting parallel virtual machine (PVM) and/or message passing interface (MPI). It is a continuation of the LAPACK project, which designed and produced analogous software for workstations, vector supercomputers, and shared memory parallel computers. Both libraries contain routines for solving systems of linear equations, least squares problems, and eigenvalue problems. The goals of both projects are efficiency, scalability, reliability, portability, flexibility, and ease of use.ScaLAPACK includes routines for the solution of dense, band, and tridiagonal linear systems of equations, condition estimation and iterative refinement, for LU and Cholesky factorization, matrix inversion, full-rank linear least squares problems, orthogonal and generalized orthogonal factorizations, orthogonal transformation routines, reductions to upper Hessenberg, bidiagonal and tridiagonal form, reduction of a symmetric-definite/Hermitian-definite generalized eigenproblem to standard form, the symmetric/Hermitian, generalized symmetric/Hermitian, and the nonsymmetric eigenproblem. Prototype codes are provided for out-of-core solvers for LU, Cholesky, and QR, the matrix sign function for eigenproblems, and an HPF interface to a subset of ScaLAPACK routines.Software is available in single precision real, double precision real, single precision complex, and double precision complex. The software has been written to be portable across a wide range of distributed-memory environments such as the Cray T3, IBM SP, Intel series, TM CM-5, clusters of workstations, and any system for which PVM or MPI is available.Each Users’ Guide includes a CD-ROM containing the HTML version of the ScaLAPACK Users’ Guide, the source code for the package, testing and timing programs, prebuilt version of the library for a number of computers, example programs, and the full set of LAPACK Working Notes. Homepage: http://www.netlib.org/scalapack/index.html Keywords: users’ guide; program library; ScaLAPACK; linear algebra package; software for workstations; vector supercomputers; shared memory parallel computers Related Software: LAPACK; BLAS; PLAPACK; MPI; PETSc; MUMPS; ARPACK; mctoolbox; LINPACK; MAGMA; Matlab; ATLAS; EISPACK; ELPA; PLASMA; JDQZ; JDQR; Trilinos; Algorithm 679; Elemental Referenced in: 402 Publications
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### Referenced by 800 Authors

 32 Dongarra, Jack J. 19 Quintana-Ortí, Enrique S. 17 Demmel, James Weldon 14 Benner, Peter 11 Quintana-Ortí, Gregorio 10 Hernández, Vicente G. 10 Kågström, Bo 10 van de Geijn, Robert Alexander 10 Vidal, Antonio Manuel 8 D’Azevedo, Eduardo F. 7 Choi, Jaeyoung 7 Robert, Yves 7 Walker, David W. 6 Alonso, Pedro 6 Bientinesi, Paolo 6 Granat, Robert A. 6 Ibáñez González, Jacinto Javier 6 Peinado, Jesús 6 Vömel, Christof 5 Arias, Enrique 5 Drmač, Zlatko 5 Duff, Iain S. 5 Hammarling, Sven J. 5 Holtz, Olga 5 Kontoghiorghes, Erricos John 5 Langou, Julien 5 Marques, Osni A. 5 Petitet, Antoine 5 Sameh, Ahmed H. 4 Amestoy, Patrick R. 4 Arndt, Daniel 4 Baboulin, Marc 4 Badía, José M. 4 Bangerth, Wolfgang 4 Beaumont, Olivier 4 Byers, Ralph 4 de Hoop, Maarten V. 4 Drummond, L. Anthony 4 Grigori, Laura 4 Heister, Timo 4 Heltai, Luca 4 Heroux, Michael A. 4 Hoshi, Takeo 4 Kronbichler, Martin 4 Kurzak, Jakub 4 Li, Xiaoye Sherry 4 Lin, Lin 4 Ltaief, Hatem 4 Luszczek, Piotr 4 Maier, Matthias Sebastian 4 Mayo, Rafael 4 Pelteret, Jean-Paul 4 Rastello, Fabrice 4 Rouet, François-Henry 4 Turcksin, Bruno 4 Xia, Jianlin 3 Ballard, Grey M. 3 Bečka, Martin 3 Boudet, Vincent 3 Casanova, Henri 3 Fehling, Marc 3 Fukuda, Mituhiro 3 Galiano, Vicente 3 Gates, Mark 3 Gratton, Serge 3 Guarracino, Mario Rosario 3 Gustavson, Fred G. 3 Haidar, Azzam 3 Henry, Greg M. 3 Katagiri, Takahiro 3 Keyes, David Elliot 3 Kolberg, Mariana Luderitz 3 Kressner, Daniel 3 L’Excellent, Jean-Yves 3 Manguoglu, Murat 3 Margenov, Svetozar D. 3 Migallón, Violeta 3 Okša, Gabriel 3 Parlett, Beresford Neill 3 Penadés, José 3 Perla, Francesca 3 Román, Jose E. 3 Ruiz, Pedro A. 3 Schwartz, Oded 3 Stoykov, Stanislav 3 Vajteršic, Marián 3 Van der Vorst, Henk Albertus 3 Van Zee, Field Garritt 3 Vasconcelos, Paulo Beleza 3 Whaley, R. Clint 3 Yamashita, Makoto 3 Yamazaki, Ichitaro 3 Yang, Chao 3 YarKhan, Asim 3 Zanetti, Paolo 2 Adlerborn, Björn 2 Aiba, Nobuyuki 2 Anitescu, Mihai 2 Bai, Zhaojun 2 Bartlett, Roscoe A. ...and 700 more Authors
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### Referenced in 106 Serials

 43 ACM Transactions on Mathematical Software 32 SIAM Journal on Scientific Computing 16 Journal of Computational Physics 16 Journal of Computational and Applied Mathematics 15 Parallel Computing 14 Journal of Parallel and Distributed Computing 13 Computer Physics Communications 10 SIAM Journal on Matrix Analysis and Applications 6 Journal of Fluid Mechanics 5 International Journal of Parallel Programming 5 Numerical Linear Algebra with Applications 4 Computers & Mathematics with Applications 4 Computer Methods in Applied Mechanics and Engineering 4 Concurrency: Practice and Experience 4 Engineering Analysis with Boundary Elements 4 Journal of Numerical Mathematics 4 Software - Environments - Tools 3 Computers and Fluids 3 Applied Mathematics and Computation 3 International Journal for Numerical Methods in Engineering 3 Mathematics and Computers in Simulation 3 Numerische Mathematik 3 Applied Numerical Mathematics 3 Algorithmica 3 Journal of Scientific Computing 3 The Journal of Supercomputing 3 Numerical Algorithms 3 Linear Algebra and its Applications 3 Optimization Methods & Software 3 Concurrency and Computation: Practice & Experience 3 Parallel Processing Letters 2 Japan Journal of Industrial and Applied Mathematics 2 International Journal of Foundations of Computer Science 2 SIAM Review 2 Advances in Engineering Software 2 Journal of Functional Programming 2 Mathematical Problems in Engineering 2 International Journal of Applied Mathematics and Computer Science 2 The ANZIAM Journal 2 Acta Numerica 2 International Journal of Parallel, Emergent and Distributed Systems 2 Statistics and Computing 2 S$$\vec{\text{e}}$$MA Journal 2 Graduate Texts in Physics 1 Information Processing Letters 1 Journal of the Franklin Institute 1 BIT 1 IEEE Transactions on Computers 1 Journal of Computer and System Sciences 1 Journal of the Operations Research Society of Japan 1 Programming and Computer Software 1 Theoretical Computer Science 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Physica D 1 Journal of Computer Science and Technology 1 Computers & Operations Research 1 COMPEL 1 Mathematical and Computer Modelling 1 FGCS. Future Generation Computer Systems 1 Applications of Mathematics 1 Journal of Non-Newtonian Fluid Mechanics 1 Computational Statistics and Data Analysis 1 Mathematical Programming. Series A. Series B 1 SIAM Journal on Optimization 1 Computational Optimization and Applications 1 Computational Economics 1 Computational and Applied Mathematics 1 ETNA. Electronic Transactions on Numerical Analysis 1 Journal of Geodesy 1 Journal of Mathematical Chemistry 1 Parallel Algorithms and Applications 1 Computing and Visualization in Science 1 International Journal of Computational Fluid Dynamics 1 Nonlinear Dynamics 1 Journal of Combinatorial Optimization 1 Journal of Scheduling 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Mathematical and Computer Modelling of Dynamical Systems 1 Informatica (Vilnius) 1 International Journal of Numerical Modelling 1 Computational Geosciences 1 Combustion Theory and Modelling 1 Lobachevskii Journal of Mathematics 1 International Journal of Modern Physics C 1 Journal of Computational and Applied Mechanics 1 International Journal of Pure and Applied Mathematics 1 Information 1 Computer Languages, Systems & Structures 1 Quantum Information Processing 1 Internet Mathematics 1 SORT. Statistics and Operations Research Transactions 1 Journal of Statistical Mechanics: Theory and Experiment 1 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Advances in Computational Economics 1 Bericht. Universität Jyväskylä. Mathematisches Institut 1 International Series in Operations Research & Management Science 1 Lecture Notes in Computational Science and Engineering 1 Mathematics in Computer Science 1 International Journal of Energy, Environment and Economics ...and 6 more Serials
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### Referenced in 28 Fields

 280 Numerical analysis (65-XX) 126 Computer science (68-XX) 40 Linear and multilinear algebra; matrix theory (15-XX) 27 Fluid mechanics (76-XX) 18 Operations research, mathematical programming (90-XX) 15 Quantum theory (81-XX) 13 Statistics (62-XX) 11 Statistical mechanics, structure of matter (82-XX) 11 Systems theory; control (93-XX) 9 Partial differential equations (35-XX) 9 Mechanics of deformable solids (74-XX) 8 Optics, electromagnetic theory (78-XX) 6 Geophysics (86-XX) 6 Biology and other natural sciences (92-XX) 4 General and overarching topics; collections (00-XX) 4 Ordinary differential equations (34-XX) 3 Number theory (11-XX) 3 Integral equations (45-XX) 3 Astronomy and astrophysics (85-XX) 2 Probability theory and stochastic processes (60-XX) 2 Relativity and gravitational theory (83-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of particles and systems (70-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)