ARPACK

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.


References in zbMATH (referenced in 811 articles , 1 standard article )

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  1. Engström, C.; Giani, S.; Grubišić, L.: Higher order composite DG approximations of Gross-Pitaevskii ground state: benchmark results and experiments (2022)
  2. Achdou, Yves; Laurière, Mathieu; Lions, Pierre-Louis: Optimal control of conditioned processes with feedback controls (2021)
  3. Al Daas, Hussam; Grigori, Laura; Jolivet, Pierre; Tournier, Pierre-Henri: A multilevel Schwarz preconditioner based on a hierarchy of robust coarse spaces (2021)
  4. Barnafi, Nicolás; Zunino, Paolo; Dedè, Luca; Quarteroni, Alfio: Mathematical analysis and numerical approximation of a general linearized poro-hyperelastic model (2021)
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  6. Courrieu, Pierre: On the convergence of rank-one multi-target linear regression (2021)
  7. Cowen, Lenore; Devkota, Kapil; Hu, Xiaozhe; Murphy, James M.; Wu, Kaiyi: Diffusion state distances: multitemporal analysis, fast algorithms, and applications to biological networks (2021)
  8. Giani, Stefano; Hakula, Harri: On effects of perforated domains on parameter-dependent free vibration (2021)
  9. Hokanson, Jeffrey M.; Constantine, Paul G.: A Lipschitz matrix for parameter reduction in computational science (2021)
  10. Kalantzis, Vassilis; Xi, Yuanzhe; Horesh, Lior: Fast randomized non-Hermitian eigensolvers based on rational filtering and matrix partitioning (2021)
  11. Kileel, Joe; Moscovich, Amit; Zelesko, Nathan; Singer, Amit: Manifold learning with arbitrary norms (2021)
  12. Mathieu Besancon, Alejandro Carderera, Sebastian Pokutta: FrankWolfe.jl: a high-performance and flexible toolbox for Frank-Wolfe algorithms and Conditional Gradients (2021) arXiv
  13. Roddick, Greg: Computation of scattering matrices and their derivatives for waveguides (2021)
  14. Yurtsever, Alp; Tropp, Joel A.; Fercoq, Olivier; Udell, Madeleine; Cevher, Volkan: Scalable semidefinite programming (2021)
  15. Adam, Nicolas; Le Tallec, Patrick; Zarroug, Malek: Multipatch isogeometric mortar methods for thick shells (2020)
  16. Arndt, Daniel; Bangerth, Wolfgang; Blais, Bruno; Clevenger, Thomas C.; Fehling, Marc; Grayver, Alexander V.; Heister, Timo; Heltai, Luca; Kronbichler, Martin; Maier, Matthias; Munch, Peter; Pelteret, Jean-Paul; Rastak, Reza; Tomas, Ignacio; Turcksin, Bruno; Wang, Zhuoran; Wells, David: The deal.II library, version 9.2 (2020)
  17. Barnett, Alex; Greengard, Leslie; Hagstrom, Thomas: High-order discretization of a stable time-domain integral equation for 3D acoustic scattering (2020)
  18. Chekroun, Mickaël D.; Tantet, Alexis; Dijkstra, Henk A.; Neelin, J. David: Ruelle-Pollicott resonances of stochastic systems in reduced state space. Part I: Theory (2020)
  19. Dubois, François; Lallemand, Pierre; Tekitek, Mohamed Mahdi: On anti bounce back boundary condition for lattice Boltzmann schemes (2020)
  20. Ezvan, Olivier; Zeng, Xiaoshu; Ghanem, Roger; Gencturk, Bora: Multiscale modal analysis of fully-loaded spent nuclear fuel canisters (2020)

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