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 780 articles , 1 standard article )

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  1. 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)
  2. Ezvan, Olivier; Zeng, Xiaoshu; Ghanem, Roger; Gencturk, Bora: Multiscale modal analysis of fully-loaded spent nuclear fuel canisters (2020)
  3. Gedicke, Joscha; Khan, Arbaz: Divergence-conforming discontinuous Galerkin finite elements for Stokes eigenvalue problems (2020)
  4. Girardi, Maria; Padovani, Cristina; Pellegrini, Daniele; Porcelli, Margherita; Robol, Leonardo: Finite element model updating for structural applications (2020)
  5. Goulart, Paul J.; Nakatsukasa, Yuji; Rontsis, Nikitas: Accuracy of approximate projection to the semidefinite cone (2020)
  6. Kalantzis, Vassilis: A spectral Newton-Schur algorithm for the solution of symmetric generalized eigenvalue problems (2020)
  7. Kpadonou, Félix; Chaillat, Stéphanie; Ciarlet, Patrick: On the efficiency of nested GMRES preconditioners for 3D acoustic and elastodynamic (\mathcalH)-matrix accelerated boundary element methods (2020)
  8. Pfister, Jean-Lou; Marquet, O.: Fluid-structure stability analyses and nonlinear dynamics of flexible splitter plates interacting with a circular cylinder flow (2020)
  9. Tantet, Alexis; Chekroun, Mickaël D.; Dijkstra, Henk A.; Neelin, J. David: Ruelle-Pollicott resonances of stochastic systems in reduced state space. Part II: Stochastic Hopf bifurcation (2020)
  10. Tantet, Alexis; Chekroun, Mickaël D.; Neelin, J. David; Dijkstra, Henk A.: Ruelle-Pollicott resonances of stochastic systems in reduced state space. Part III: Application to the Cane-Zebiak model of the El Niño-southern oscillation (2020)
  11. Uschmajew, André; Vandereycken, Bart: Geometric methods on low-rank matrix and tensor manifolds (2020)
  12. Adachi, Satoru; Nakatsukasa, Yuji: Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint (2019)
  13. Adam, Lukáš; Hintermüller, Michael; Peschka, Dirk; Surowiec, Thomas M.: Optimization of a multiphysics problem in semiconductor laser design (2019)
  14. Andreotti, Eleonora; Edelmann, Dominik; Guglielmi, Nicola; Lubich, Christian: Constrained graph partitioning via matrix differential equations (2019)
  15. Aravkin, Aleksandr Y.; Burke, James V.; Drusvyatskiy, Dmitry; Friedlander, Michael P.; Roy, Scott: Level-set methods for convex optimization (2019)
  16. Arndt, Daniel; Bangerth, Wolfgang; Clevenger, Thomas C.; Davydov, Denis; Fehling, Marc; Garcia-Sanchez, Daniel; Harper, Graham; Heister, Timo; Heltai, Luca; Kronbichler, Martin; Kynch, Ross Maguire; Maier, Matthias; Pelteret, Jean-Paul; Turcksin, Bruno; Wells, David: The deal.II library, Version 9.1 (2019)
  17. Avron, Haim; Druinsky, Alex; Toledo, Sivan: Spectral condition-number estimation of large sparse matrices. (2019)
  18. Benner, Peter; Mitchell, Tim: Extended and improved criss-cross algorithms for computing the spectral value set abscissa and radius (2019)
  19. Boffi, Daniele; Gastaldi, Lucia; Rodríguez, Rodolfo; Šebestová, Ivana: A posteriori error estimates for Maxwell’s eigenvalue problem (2019)
  20. Brynjell-Rahkola, Mattias; Hanifi, Ardeshir; Henningson, Dan S.: On the stability of a Blasius boundary layer subject to localised suction (2019)

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