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 731 articles , 1 standard article )

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  1. Adachi, Satoru; Nakatsukasa, Yuji: Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint (2019)
  2. Adam, Lukáš; Hintermüller, Michael; Peschka, Dirk; Surowiec, Thomas M.: Optimization of a multiphysics problem in semiconductor laser design (2019)
  3. Andreotti, Eleonora; Edelmann, Dominik; Guglielmi, Nicola; Lubich, Christian: Constrained graph partitioning via matrix differential equations (2019)
  4. Camps, Daan; Meerbergen, Karl; Vandebril, Raf: An implicit filter for rational Krylov using core transformations (2019)
  5. De Marchi, S.; Martínez, A.; Perracchione, E.: Fast and stable rational RBF-based partition of unity interpolation (2019)
  6. Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, Ziyun: A fast hierarchically preconditioned eigensolver based on multiresolution matrix decomposition (2019)
  7. Huang, Wei-Qiang; Lin, Wen-Wei; Lu, Henry Horng-Shing; Yau, Shing-Tung: iSIRA: integrated shift-invert residual Arnoldi method for graph Laplacian matrices from big data (2019)
  8. Lambers, James V.; Sumner, Amber C.: Explorations in numerical analysis (2019)
  9. Li, Ruipeng; Xi, Yuanzhe; Erlandson, Lucas; Saad, Yousef: The eigenvalues slicing library (EVSL): algorithms, implementation, and software (2019)
  10. Matteo Ravasi, Ivan Vasconcelos: PyLops - A Linear-Operator Python Library for large scale optimization (2019) arXiv
  11. N. Benjamin Erichson, Sergey Voronin, Steven L. Brunton, J. Nathan Kutz: Randomized Matrix Decompositions Using R (2019) not zbMATH
  12. Noschese, Silvia; Reichel, Lothar: Computing unstructured and structured polynomial pseudospectrum approximations (2019)
  13. Winkelmann, Jan; Springer, Paul; Di Napoli, Edoardo: ChASE: Chebyshev accelerated subspace iteration eigensolver for sequences of Hermitian eigenvalue problems (2019)
  14. Alfonso Iodice D’Enza, Angelos Markos, Davide Buttarazzi: The idm Package: Incremental Decomposition Methods in R (2018) not zbMATH
  15. Alzetta, Giovanni; Arndt, Daniel; Bangerth, Wolfgang; Boddu, Vishal; Brands, Benjamin; Davydov, Denis; Gassmöller, Rene; Heister, Timo; Heltai, Luca; Kormann, Katharina; Kronbichler, Martin; Maier, Matthias; Pelteret, Jean-Paul; Turcksin, Bruno; Wells, David: The deal.II library, version 9.0 (2018)
  16. Arko Roy, Sukla Pal, S. Gautam, D. Angom, P. Muruganandam: FACt: FORTRAN toolbox for calculating fluctuations in atomic condensates (2018) arXiv
  17. Bergamaschi, Luca; Bozzo, Enrico: Computing the smallest eigenpairs of the graph Laplacian (2018)
  18. Birgin, E. G.; Haeser, G.; Ramos, Alberto: Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points (2018)
  19. Bosch, Jessica; Klamt, Steffen; Stoll, Martin: Generalizing diffuse interface methods on graphs: nonsmooth potentials and hypergraphs (2018)
  20. Bosner, Nela; Bujanović, Zvonimir; Drmač, Zlatko: Parallel solver for shifted systems in a hybrid CPU-GPU framework (2018)

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