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; MPI; R; Algorithm 679; MKL; CUDA; PLAPACK
Cited in: 1,647 Publications
This software is also referenced in ORMS.
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Cited by 2,644 Authors

55 Dongarra, Jack J.
37 Demmel, James Weldon
32 Quintana-Ortí, Enrique S.
31 Higham, Nicholas J.
30 Benner, Peter
24 Drmač, Zlatko
24 van de Geijn, Robert Alexander
22 Mehrmann, Volker
22 Quintana-Ortí, Gregorio
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 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 Hernández, Vicente G.
8 Li, Rencang
8 Luszczek, Piotr
8 Manocha, Dinesh
8 Petkov, Petko Hr.
8 Walker, David W.
7 Bosner, Nela
7 Chu, Delin
7 Dhillon, Inderjit S.
7 Giraud, Luc
7 Haidar, Azzam
7 Ibáñez González, Jacinto Javier
7 Keyes, David Elliot
7 Koev, Plamen
7 Konstantinov, Mikhail Mikhajlov
7 Paprzycki, Marcin
7 Petitet, Antoine
7 Sherwin, Spencer J.
7 Slapničar, Ivan
7 Tisseur, Françoise
7 Van Huffel, Sabine
7 Van Zee, Field Garritt
7 Ward, Michael J.
7 Watson, Layne Terry
6 Bangerth, Wolfgang
6 Barlow, Jesse L.
6 Berry, Michael W.
6 Buttari, Alfredo
6 Chandrasekaran, Shivkumar
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 Sastre, Jorge
6 Song, Chongmin
6 Van der Vorst, Henk Albertus
6 Wei, Juncheng
6 Yamazaki, Ichitaro
5 Arndt, Daniel
5 Avron, Haim
5 Baboulin, Marc
5 Calvetti, Daniela
5 Choi, Jaeyoung
5 Corless, Robert Malcolm
5 di Serafino, Daniela
5 Dopico, Froilán M.
5 Eijkhout, Victor L.
5 Gansterer, Wilfried N.
5 Granat, Robert A.
5 Gunnels, John A.
5 Heister, Timo
5 Heltai, Luca
5 Heroux, Michael A.
5 Holtz, Olga
5 Hopkins, Tim R.
5 Jonsson, Isak
5 Kolokolnikov, Theodore
5 Krishnan, Shankar M.
5 Kronbichler, Martin
5 Lemmerling, Philippe
...and 2,544 more Authors
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Cited in 288 Serials

132 ACM Transactions on Mathematical Software
117 SIAM Journal on Scientific Computing
82 Journal of Computational Physics
76 SIAM Journal on Matrix Analysis and Applications
63 Journal of Computational and Applied Mathematics
63 Linear Algebra and its Applications
56 Computer Physics Communications
39 Numerical Linear Algebra with Applications
37 Computer Methods in Applied Mechanics and Engineering
27 Numerical Algorithms
26 Computers & Mathematics with Applications
22 International Journal for Numerical Methods in Engineering
21 Parallel Computing
20 Applied Mathematics and Computation
17 Computers and Fluids
16 BIT
16 Applied Numerical Mathematics
15 Numerische Mathematik
15 Engineering Analysis with Boundary Elements
14 Journal of Scientific Computing
12 ETNA. Electronic Transactions on Numerical Analysis
12 Optimization Methods & Software
11 Journal of Fluid Mechanics
10 Computational Optimization and Applications
9 Computing
9 SIAM Journal on Optimization
9 Software - Environments - Tools
8 Computational Mechanics
8 Computational Statistics and Data Analysis
7 Mathematics of Computation
7 Mathematics and Computers in Simulation
7 Physica D
7 Japan Journal of Industrial and Applied Mathematics
7 Advances in Computational Mathematics
6 International Journal for Numerical Methods in Fluids
6 European Journal of Operational Research
6 SIAM Review
6 Mathematical Programming. Series A. Series B
6 Journal of Machine Learning Research (JMLR)
6 Acta Numerica
6 Mathematical Programming Computation
5 Journal of Symbolic Computation
5 Journal of Parallel and Distributed Computing
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 Journal of Optimization Theory and Applications
4 International Journal of Parallel Programming
4 Mathematical and Computer Modelling
4 Machine Learning
4 Journal of Global Optimization
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 Journal of Numerical Mathematics
4 Parallel Processing Letters
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 SIAM Journal on Scientific and Statistical Computing
3 Computer Aided Geometric Design
3 Numerical Methods for Partial Differential Equations
3 Applied Mathematics Letters
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 Journal of Geodesy
3 Mathematical Communications
3 Computational Geosciences
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 Communications in Computational Physics
3 Statistics and Computing
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
2 Mathematical Biosciences
2 Nonlinearity
2 Physics Letters. A
2 Calcolo
2 Information Sciences
2 Programming and Computer Software
2 SIAM Journal on Control and Optimization
...and 188 more Serials
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Cited in 49 Fields

1,187 Numerical analysis (65-XX)
227 Linear and multilinear algebra; matrix theory (15-XX)
218 Computer science (68-XX)
173 Fluid mechanics (76-XX)
125 Partial differential equations (35-XX)
97 Operations research, mathematical programming (90-XX)
86 Mechanics of deformable solids (74-XX)
70 Quantum theory (81-XX)
65 Systems theory; control (93-XX)
64 Statistics (62-XX)
51 Ordinary differential equations (34-XX)
48 Statistical mechanics, structure of matter (82-XX)
42 Biology and other natural sciences (92-XX)
33 Optics, electromagnetic theory (78-XX)
22 General and overarching topics; collections (00-XX)
22 Calculus of variations and optimal control; optimization (49-XX)
21 Dynamical systems and ergodic theory (37-XX)
20 Geophysics (86-XX)
18 Classical thermodynamics, heat transfer (80-XX)
17 Information and communication theory, circuits (94-XX)
16 Approximations and expansions (41-XX)
14 Field theory and polynomials (12-XX)
14 Mechanics of particles and systems (70-XX)
12 Probability theory and stochastic processes (60-XX)
12 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
11 Combinatorics (05-XX)
11 Functions of a complex variable (30-XX)
11 Operator theory (47-XX)
10 Real functions (26-XX)
10 Astronomy and astrophysics (85-XX)
9 Integral equations (45-XX)
8 Commutative algebra (13-XX)
8 Relativity and gravitational theory (83-XX)
6 Algebraic geometry (14-XX)
4 History and biography (01-XX)
4 Harmonic analysis on Euclidean spaces (42-XX)
3 Global analysis, analysis on manifolds (58-XX)
2 Number theory (11-XX)
2 Potential theory (31-XX)
2 Special functions (33-XX)
2 Difference and functional equations (39-XX)
2 Integral transforms, operational calculus (44-XX)
2 Convex and discrete geometry (52-XX)
2 Differential geometry (53-XX)
2 Mathematics education (97-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)

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