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 Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year ARPACK user’s guide. Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. Zbl 0901.65021Lehoucq, R. B.; Sorensen, D. C.; Yang, C. 1998 all top 5 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 all top 5 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 2 Physics Letters. B 2 Automatica 2 Computing 2 Journal of Optimization Theory and Applications 2 Physica D 2 Computational Mechanics 2 Computational Statistics 2 Applied Mathematical Modelling 2 Journal of Non-Newtonian Fluid Mechanics 2 Computational Statistics and Data Analysis 2 Journal of Nonlinear Science 2 Nuclear Physics. B. Proceedings Supplements 2 Computational and Applied Mathematics 2 Journal of Mathematical Chemistry 2 Parallel Algorithms and Applications 2 Computing and Visualization in Science 2 International Journal of Computational Fluid Dynamics 2 Taiwanese Journal of Mathematics 2 Chaos 2 International Journal of Applied Mathematics and Computer Science 2 Computational Geosciences 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 2 Journal of Computational Acoustics 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 GAMM-Mitteilungen 2 Software - Environments - Tools 2 SIAM Journal on Imaging Sciences 2 Advances in Applied Mathematics and Mechanics 2 S\(\vec{\text{e}}\)MA Journal 2 SIAM Journal on Mathematics of Data Science 2 Journal of Computational and Theoretical Transport 1 International Journal of Modern Physics A 1 Communications in Mathematical Physics 1 International Journal of Control 1 Letters in Mathematical Physics 1 Linear and Multilinear Algebra 1 Mathematical Biosciences 1 Physica A 1 Molecular Simulation 1 Prikladnaya Matematika i Mekhanika 1 Fortschritte der Physik 1 Applied Mathematics and Optimization ...and 90 more Serials all top 5 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) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral equations (45-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year