swMATH ID: 4218
Software Authors: Lehoucq; Sorensen; Yang
Description: ARPACK is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems. The package is designed to compute a few eigenvalues and corresponding eigenvectors of a general n by n matrix A. It is most appropriate for large sparse or structured matrices A where structured means that a matrix-vector product w <- Av requires order n rather than the usual order n2 floating point operations. This software is based upon an algorithmic variant of the Arnoldi process called the Implicitly Restarted Arnoldi Method (IRAM). When the matrix A is symmetric it reduces to a variant of the Lanczos process called the Implicitly Restarted Lanczos Method (IRLM). These variants may be viewed as a synthesis of the Arnoldi/Lanczos process with the Implicitly Shifted QR technique that is suitable for large scale problems. For many standard problems, a matrix factorization is not required. Only the action of the matrix on a vector is needed.
ARPACK software is capable of solving large scale symmetric, nonsymmetric, and generalized eigenproblems from significant application areas. The software is designed to compute a few (k) eigenvalues with user specified features such as those of largest real part or largest magnitude. Storage requirements are on the order of n*k locations. No auxiliary storage is required. A set of Schur basis vectors for the desired k-dimensional eigen-space is computed which is numerically orthogonal to working precision. Numerically accurate eigenvectors are available on request.
Homepage: http://www.caam.rice.edu/software/ARPACK/
Related Software: eigs; JDQZ; JDQR; LAPACK; Matlab; Eigtool; IRAM; PETSc; SLEPc; MUMPS; lobpcg.m; SparseMatrix; TRLan; mctoolbox; UMFPACK; ScaLAPACK; PRIMME; BLAS; PARDISO; PROPACK
Cited in: 836 Publications
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Cited by 1,454 Authors

23 Sorensen, Danny C.
17 Saad, Yousef
15 Mehrmann, Volker
14 Kressner, Daniel
14 Lehoucq, Richard B.
13 Giani, Stefano
13 Reichel, Lothar
12 Guglielmi, Nicola
11 Schmid, Peter Joseph
10 Zhou, Yunkai
8 Bai, Zhaojun
8 Bergamaschi, Luca
8 Golub, Gene Howard
8 Meerbergen, Karl
8 Salinger, Andrew G.
8 Stathopoulos, Andreas
7 Baglama, James
7 Embree, Mark
7 Pini, Giorgio
7 Román, Jose E.
7 Voss, Heinrich
6 Alizard, Frédéric
6 Arbenz, Peter
6 Bangerth, Wolfgang
6 Benner, Peter
6 Heister, Timo
6 Heltai, Luca
6 Henningson, Dan S.
6 Kronbichler, Martin
6 Lin, Wen-Wei
6 Lubich, Christian
6 Maier, Matthias Sebastian
6 Marquet, Olivier
6 Robinet, Jean-Christophe
6 Schlatter, Philipp
6 Simoncini, Valeria
6 Turcksin, Bruno
6 Ye, Qiang
5 Arndt, Daniel
5 Bekas, Constantine
5 Calvetti, Daniela
5 Gattringer, Christof
5 Gedicke, Joscha
5 Giraud, Luc
5 Graham, Ivan G.
5 Hall, Edward J. C.
5 Hetmaniuk, Ulrich L.
5 Huang, Tsungming
5 Międlar, Agnieszka
5 Nakatsukasa, Yuji
5 Pelteret, Jean-Paul
5 Rojas, Marielba
5 Sipp, Denis
5 Yang, Chao
5 Zhang, Lei-Hong
4 Buchot, Jean-Marie
4 Daube, Olivier
4 Davydov, Denis
4 Dijkstra, Henk A.
4 Dongarra, Jack J.
4 Eldén, Lars
4 Gallopoulos, Efstratios
4 Giannakis, Dimitrios
4 Higham, Nicholas J.
4 Houston, Paul
4 Huisinga, Wilhelm
4 Jia, Zhongxiao
4 Jolivet, Pierre
4 Labrosse, Gérard
4 Lang, Christian B.
4 Leriche, Emmanuel
4 Liu, Xin
4 Lu, Ding
4 Net, Marta
4 Neuberger, John M.
4 Overton, Michael L.
4 Pawlowski, Roger P.
4 Salas, Jesús
4 Sartoretto, Flavio
4 Schütte, Christof
4 Shadid, John N.
4 Simon, Horst D.
4 Tantet, Alexis
4 Tisseur, Françoise
4 Trefethen, Lloyd Nicholas
4 Vandereycken, Bart
4 Wang, Lin-Wang
4 Wen, Zaiwen
4 Wu, Kesheng
4 Xi, Yuanzhe
4 Zhang, Yin
3 Apel, Thomas
3 Bagheri, Shervin
3 Bhuruth, Muddun
3 Bonito, Andrea
3 Cadou, Jean-Marc
3 Carpentieri, Bruno
3 Carstensen, Carsten
3 Çetinbaş, Murat
3 Chekroun, Mickaël D.
...and 1,354 more Authors
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Cited in 190 Serials

68 SIAM Journal on Scientific Computing
60 Journal of Computational Physics
54 Journal of Fluid Mechanics
52 SIAM Journal on Matrix Analysis and Applications
30 Journal of Computational and Applied Mathematics
23 Linear Algebra and its Applications
21 Numerical Linear Algebra with Applications
19 Computer Methods in Applied Mechanics and Engineering
18 ACM Transactions on Mathematical Software
15 Computer Physics Communications
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14 International Journal for Numerical Methods in Engineering
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12 International Journal for Numerical Methods in Fluids
12 Journal of Scientific Computing
10 BIT
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7 Journal of Statistical Physics
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7 Mathematical Programming. Series A. Series B
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4 Theoretical and Computational Fluid Dynamics
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4 SIAM Journal on Applied Dynamical Systems
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4 Journal of Physics A: Mathematical and Theoretical
3 Geophysical and Astrophysical Fluid Dynamics
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3 Japan Journal of Industrial and Applied Mathematics
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3 Annals of Physics
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3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
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3 Communications in Numerical Methods in Engineering
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3 European Journal of Mechanics. B. Fluids
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2 IMA Journal of Numerical Analysis
2 International Journal of Heat and Mass Transfer
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2 Nonlinearity
2 Nuclear Physics. B
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Cited in 45 Fields

547 Numerical analysis (65-XX)
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89 Linear and multilinear algebra; matrix theory (15-XX)
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45 Computer science (68-XX)
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23 Biology and other natural sciences (92-XX)
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12 Geophysics (86-XX)
11 Combinatorics (05-XX)
7 Mechanics of particles and systems (70-XX)
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5 Information and communication theory, circuits (94-XX)
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2 History and biography (01-XX)
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