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LAPACK

swMATH ID: 503
Software Authors: LAPACK team: lapack@cs.utk.edu
Description: LAPACK is written in Fortran 90 and provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also provided, as are related computations such as reordering of the Schur factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse matrices. In all areas, similar functionality is provided for real and complex matrices, in both single and double precision.
The original goal of the LAPACK project was to make the widely used EISPACK and LINPACK libraries run efficiently on shared-memory vector and parallel processors. On these machines, LINPACK and EISPACK are inefficient because their memory access patterns disregard the multi-layered memory hierarchies of the machines, thereby spending too much time moving data instead of doing useful floating-point operations. LAPACK addresses this problem by reorganizing the algorithms to use block matrix operations, such as matrix multiplication, in the innermost loops. These block operations can be optimized for each architecture to account for the memory hierarchy, and so provide a transportable way to achieve high efficiency on diverse modern machines. We use the term ”transportable” instead of ”portable” because, for fastest possible performance, LAPACK requires that highly optimized block matrix operations be already implemented on each machine.
LAPACK routines are written so that as much as possible of the computation is performed by calls to the Basic Linear Algebra Subprograms (BLAS). LAPACK is designed at the outset to exploit the Level 3 BLAS — a set of specifications for Fortran subprograms that do various types of matrix multiplication and the solution of triangular systems with multiple right-hand sides. Because of the coarse granularity of the Level 3 BLAS operations, their use promotes high efficiency on many high-performance computers, particularly if specially coded implementations are provided by the manufacturer.
Highly efficient machine-specific implementations of the BLAS are available for many modern high-performance computers. For details of known vendor- or ISV-provided BLAS, consult the BLAS FAQ. Alternatively, the user can download ATLAS to automatically generate an optimized BLAS library for the architecture. A Fortran 77 reference implementation of the BLAS is available from netlib; however, its use is discouraged as it will not perform as well as a specifically tuned implementation.
Homepage: http://www.netlib.org/lapack/
Programming Languages: FORTRAN
Keywords: orms; LAPACK software; library of FORTRAN 77 routines; nonsymmetric eigenproblem; linear least squares problems; singular value decomposition; QR and RQ factorizations; reduction of a band matrix
Related Software: BLAS; ScaLAPACK; mctoolbox; Matlab; LINPACK; ARPACK; EISPACK; CLAPACK; PETSc; SparseMatrix; JDQZ; ATLAS; JDQR; MUMPS; MKL; MPI; R; Algorithm 679; CUDA; FFTW
Cited in: 1,752 Documents
This software is also referenced in ORMS.
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Cited by 2,893 Authors

55 Dongarra, Jack J.
37 Demmel, James Weldon
33 Benner, Peter
33 Quintana-Ortí, Enrique S.
32 Higham, Nicholas J.
24 Drmač, Zlatko
24 van de Geijn, Robert Alexander
23 Quintana-Ortí, Gregorio
22 Mehrmann, Volker
18 Kågström, Bo
17 Bai, Zhaojun
15 Gu, Ming
15 Kressner, Daniel
15 Lang, Bruno
12 Bientinesi, Paolo
12 Hammarling, Sven J.
12 Lehoucq, Richard B.
12 Zlatev, Zahari
11 Duff, Iain S.
11 Gustavson, Fred G.
11 Toledo, Sivan
11 Vidal, Antonio Manuel
11 Waśniewski, Jerzy
10 Bischof, Christian H.
10 Li, Rencang
10 Parlett, Beresford Neill
10 Tomov, Stanimire Z.
10 Vömel, Christof
9 Byers, Ralph
9 Kurzak, Jakub
9 Ltaief, Hatem
9 Sorensen, Danny C.
8 Aishima, Kensuke
8 Alonso, Pedro
8 Bangerth, Wolfgang
8 Hernández, Vicente G.
8 Ibáñez González, Jacinto Javier
8 Koev, Plamen
8 Luszczek, Piotr
8 Manocha, Dinesh
8 Petkov, Petko Hr.
8 Walker, David W.
8 Watson, Layne Terry
8 Yang, Chao
7 Arndt, Daniel
7 Baboulin, Marc
7 Bosner, Nela
7 Chu, Delin
7 Dhillon, Inderjit S.
7 Giraud, Luc
7 Haidar, Azzam
7 Heister, Timo
7 Heltai, Luca
7 Keyes, David Elliot
7 Konstantinov, Mikhail Mikhajlov
7 Kronbichler, Martin
7 Maier, Matthias Sebastian
7 Paprzycki, Marcin
7 Pelteret, Jean-Paul
7 Petitet, Antoine
7 Sastre, Jorge
7 Sherwin, Spencer J.
7 Slapničar, Ivan
7 Tisseur, Françoise
7 Turcksin, Bruno
7 Van Huffel, Sabine
7 Van Zee, Field Garritt
7 Ward, Michael J.
7 Xia, Jianlin
6 Barlow, Jesse L.
6 Berry, Michael W.
6 Buttari, Alfredo
6 Chandrasekaran, Shivkumar
6 Dopico, Froilán M.
6 Faragó, István
6 Foster, Leslie V.
6 Gates, Mark
6 Henry, Greg M.
6 Jessup, Elizabeth R.
6 Kontoghiorghes, Erricos John
6 Langou, Julien
6 Mach, Thomas
6 Marques, Osni A.
6 Rump, Siegfried Michael
6 Saad, Yousef
6 Song, Chongmin
6 Van der Vorst, Henk Albertus
6 Watkins, David S.
6 Wei, Juncheng
6 Yamazaki, Ichitaro
5 Amestoy, Patrick R.
5 Avron, Haim
5 Calvetti, Daniela
5 Choi, Jaeyoung
5 Corless, Robert Malcolm
5 di Serafino, Daniela
5 Eijkhout, Victor L.
5 Fehling, Marc
5 Gansterer, Wilfried N.
5 Granat, Robert A.
...and 2,793 more Authors
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Cited in 298 Serials

134 ACM Transactions on Mathematical Software
124 SIAM Journal on Scientific Computing
89 Journal of Computational Physics
84 Computer Physics Communications
78 SIAM Journal on Matrix Analysis and Applications
67 Journal of Computational and Applied Mathematics
64 Linear Algebra and its Applications
39 Computer Methods in Applied Mechanics and Engineering
39 Numerical Linear Algebra with Applications
30 Numerical Algorithms
25 Computers & Mathematics with Applications
23 International Journal for Numerical Methods in Engineering
21 Applied Mathematics and Computation
21 Parallel Computing
17 Computers and Fluids
16 BIT
16 Numerische Mathematik
16 Applied Numerical Mathematics
15 Journal of Scientific Computing
15 Engineering Analysis with Boundary Elements
12 Computational Optimization and Applications
12 ETNA. Electronic Transactions on Numerical Analysis
12 Optimization Methods & Software
11 Journal of Fluid Mechanics
10 SIAM Journal on Optimization
9 Computing
9 Mathematical Programming. Series A. Series B
9 Software - Environments - Tools
8 Mathematics and Computers in Simulation
8 Computational Mechanics
8 Computational Statistics and Data Analysis
7 Mathematics of Computation
7 Physica D
7 Japan Journal of Industrial and Applied Mathematics
7 Advances in Computational Mathematics
7 Journal of Machine Learning Research (JMLR)
7 Acta Numerica
6 International Journal for Numerical Methods in Fluids
6 European Journal of Operational Research
6 SIAM Review
6 Journal of Numerical Mathematics
6 Mathematical Programming Computation
5 Journal of Optimization Theory and Applications
5 Journal of Symbolic Computation
5 Journal of Parallel and Distributed Computing
5 Journal of Global Optimization
5 The Journal of Supercomputing
5 Physics of Fluids
5 Journal of Mathematical Chemistry
5 Concurrency and Computation: Practice & Experience
4 Acta Mechanica
4 IMA Journal of Numerical Analysis
4 Journal of Engineering Mathematics
4 Automatica
4 IEEE Transactions on Automatic Control
4 International Journal of Parallel Programming
4 Applied Mathematics Letters
4 Mathematical and Computer Modelling
4 Machine Learning
4 Journal of Mathematical Sciences (New York)
4 Russian Journal of Numerical Analysis and Mathematical Modelling
4 Parallel Algorithms and Applications
4 Computing and Visualization in Science
4 Parallel Processing Letters
4 Communications in Computational Physics
4 Statistics and Computing
4 Journal of Computational and Theoretical Transport
3 Classical and Quantum Gravity
3 Computers and Structures
3 International Journal of Solids and Structures
3 Journal of Mathematical Physics
3 SIAM Journal on Numerical Analysis
3 Theoretical Computer Science
3 SIAM Journal on Scientific and Statistical Computing
3 Computer Aided Geometric Design
3 COMPEL
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3 Annals of Operations Research
3 International Journal of Computational Geometry & Applications
3 International Journal of Computer Mathematics
3 SIAM Journal on Applied Mathematics
3 Journal of Nonlinear Science
3 Advances in Engineering Software
3 Communications in Numerical Methods in Engineering
3 Computational and Applied Mathematics
3 Journal of Geodesy
3 ELA. The Electronic Journal of Linear Algebra
3 Mathematical Communications
3 Communications in Nonlinear Science and Numerical Simulation
3 Computational Geosciences
3 Combustion Theory and Modelling
3 Archives of Computational Methods in Engineering
3 International Journal of Parallel, Emergent and Distributed Systems
3 Lecture Notes in Computational Science and Engineering
3 JSIAM Letters
2 International Journal of Control
2 International Journal of Heat and Mass Transfer
2 International Journal for Numerical and Analytical Methods in Geomechanics
2 Journal of Sound and Vibration
2 Journal of Statistical Physics
...and 198 more Serials
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Cited in 51 Fields

1,249 Numerical analysis (65-XX)
241 Linear and multilinear algebra; matrix theory (15-XX)
224 Computer science (68-XX)
189 Fluid mechanics (76-XX)
132 Partial differential equations (35-XX)
109 Operations research, mathematical programming (90-XX)
90 Mechanics of deformable solids (74-XX)
86 Quantum theory (81-XX)
73 Statistics (62-XX)
68 Systems theory; control (93-XX)
66 Statistical mechanics, structure of matter (82-XX)
51 Ordinary differential equations (34-XX)
45 Biology and other natural sciences (92-XX)
37 Optics, electromagnetic theory (78-XX)
25 Calculus of variations and optimal control; optimization (49-XX)
22 General and overarching topics; collections (00-XX)
22 Dynamical systems and ergodic theory (37-XX)
21 Geophysics (86-XX)
19 Mechanics of particles and systems (70-XX)
19 Classical thermodynamics, heat transfer (80-XX)
18 Information and communication theory, circuits (94-XX)
17 Approximations and expansions (41-XX)
15 Combinatorics (05-XX)
14 Field theory and polynomials (12-XX)
13 Operator theory (47-XX)
13 Probability theory and stochastic processes (60-XX)
13 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
12 Functions of a complex variable (30-XX)
11 Real functions (26-XX)
11 Astronomy and astrophysics (85-XX)
10 Integral equations (45-XX)
9 Commutative algebra (13-XX)
9 Relativity and gravitational theory (83-XX)
7 Algebraic geometry (14-XX)
5 History and biography (01-XX)
5 Harmonic analysis on Euclidean spaces (42-XX)
3 Special functions (33-XX)
3 Difference and functional equations (39-XX)
3 Global analysis, analysis on manifolds (58-XX)
3 Mathematics education (97-XX)
2 Number theory (11-XX)
2 Potential theory (31-XX)
2 Integral transforms, operational calculus (44-XX)
2 Functional analysis (46-XX)
2 Convex and discrete geometry (52-XX)
2 Differential geometry (53-XX)
1 Mathematical logic and foundations (03-XX)
1 Group theory and generalizations (20-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Geometry (51-XX)
1 Algebraic topology (55-XX)

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