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ARPACK

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
15 Applied Numerical Mathematics
14 International Journal for Numerical Methods in Engineering
13 Computers & Mathematics with Applications
13 Numerische Mathematik
12 International Journal for Numerical Methods in Fluids
12 Journal of Scientific Computing
10 BIT
10 Physics of Fluids
9 Computers and Fluids
9 Applied Mathematics and Computation
8 SIAM Journal on Numerical Analysis
7 Journal of Statistical Physics
7 Numerical Algorithms
7 Mathematical Programming. Series A. Series B
7 SIAM Journal on Optimization
7 ETNA. Electronic Transactions on Numerical Analysis
7 Journal of Numerical Mathematics
6 Parallel Computing
5 Inverse Problems
5 Mathematics of Computation
4 Theoretical and Computational Fluid Dynamics
4 Mathematical and Computer Modelling
4 SIAM Journal on Applied Dynamical Systems
4 Multiscale Modeling & Simulation
4 Journal of Physics A: Mathematical and Theoretical
3 Geophysical and Astrophysical Fluid Dynamics
3 Wave Motion
3 Mathematics and Computers in Simulation
3 Japan Journal of Industrial and Applied Mathematics
3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
3 Annals of Physics
3 SIAM Journal on Applied Mathematics
3 SIAM Review
3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
3 Computational Optimization and Applications
3 Communications in Numerical Methods in Engineering
3 Optimization Methods & Software
3 European Journal of Mechanics. B. Fluids
3 Communications in Computational Physics
2 IMA Journal of Numerical Analysis
2 International Journal of Heat and Mass Transfer
2 International Journal of Solids and Structures
2 Nonlinearity
2 Nuclear Physics. B
2 Physics Letters. A
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2 Journal of Non-Newtonian Fluid Mechanics
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2 Journal of Nonlinear Science
2 Nuclear Physics. B. Proceedings Supplements
2 Computational and Applied Mathematics
2 Journal of Mathematical Chemistry
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2 Computing and Visualization in Science
2 International Journal of Computational Fluid Dynamics
2 Taiwanese Journal of Mathematics
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2 International Journal of Applied Mathematics and Computer Science
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2 Concurrency and Computation: Practice & Experience
2 Discrete and Continuous Dynamical Systems. Series B
2 Journal of Machine Learning Research (JMLR)
2 Communications on Pure and Applied Analysis
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2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
2 GAMM-Mitteilungen
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2 Advances in Applied Mathematics and Mechanics
2 S\(\vec{\text{e}}\)MA Journal
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1 International Journal of Modern Physics A
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1 Mathematical Biosciences
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1 Molecular Simulation
1 Prikladnaya Matematika i Mekhanika
1 Fortschritte der Physik
1 Applied Mathematics and Optimization
...and 90 more Serials
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Cited in 45 Fields

547 Numerical analysis (65-XX)
175 Fluid mechanics (76-XX)
108 Partial differential equations (35-XX)
89 Linear and multilinear algebra; matrix theory (15-XX)
59 Mechanics of deformable solids (74-XX)
54 Optics, electromagnetic theory (78-XX)
52 Quantum theory (81-XX)
52 Operations research, mathematical programming (90-XX)
45 Computer science (68-XX)
45 Statistical mechanics, structure of matter (82-XX)
34 Dynamical systems and ergodic theory (37-XX)
32 Statistics (62-XX)
30 Systems theory; control (93-XX)
25 Probability theory and stochastic processes (60-XX)
23 Biology and other natural sciences (92-XX)
19 Ordinary differential equations (34-XX)
18 Operator theory (47-XX)
18 Classical thermodynamics, heat transfer (80-XX)
16 Calculus of variations and optimal control; optimization (49-XX)
12 Geophysics (86-XX)
11 Combinatorics (05-XX)
7 Mechanics of particles and systems (70-XX)
6 Approximations and expansions (41-XX)
5 Information and communication theory, circuits (94-XX)
4 General and overarching topics; collections (00-XX)
3 Difference and functional equations (39-XX)
3 Differential geometry (53-XX)
3 Global analysis, analysis on manifolds (58-XX)
2 History and biography (01-XX)
2 Group theory and generalizations (20-XX)
2 Functions of a complex variable (30-XX)
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2 Integral equations (45-XX)
2 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 Number theory (11-XX)
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