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 706 articles , 1 standard article )

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  1. Camps, Daan; Meerbergen, Karl; Vandebril, Raf: An implicit filter for rational Krylov using core transformations (2019)
  2. De Marchi, S.; Martínez, A.; Perracchione, E.: Fast and stable rational RBF-based partition of unity interpolation (2019)
  3. 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)
  4. Lambers, James V.; Sumner, Amber C.: Explorations in numerical analysis (2019)
  5. Noschese, Silvia; Reichel, Lothar: Computing unstructured and structured polynomial pseudospectrum approximations (2019)
  6. Arko Roy, Sukla Pal, S. Gautam, D. Angom, P. Muruganandam: FACt: FORTRAN toolbox for calculating fluctuations in atomic condensates (2018) arXiv
  7. Bergamaschi, Luca; Bozzo, Enrico: Computing the smallest eigenpairs of the graph Laplacian (2018)
  8. Birgin, E. G.; Haeser, G.; Ramos, Alberto: Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points (2018)
  9. Bosch, Jessica; Klamt, Steffen; Stoll, Martin: Generalizing diffuse interface methods on graphs: nonsmooth potentials and hypergraphs (2018)
  10. Bosner, Nela; Bujanović, Zvonimir; Drmač, Zlatko: Parallel solver for shifted systems in a hybrid CPU-GPU framework (2018)
  11. Buhr, Andreas; Smetana, Kathrin: Randomized local model order reduction (2018)
  12. Carrington, Tucker: Iterative methods for computing vibrational spectra (2018)
  13. Gedicke, Joscha; Khan, Arbaz: Arnold-Winther mixed finite elements for Stokes eigenvalue problems (2018)
  14. Gorgizadeh, Shahnam; Flisgen, Thomas; van Rienen, Ursula: Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems (2018)
  15. Goza, Andres; Colonius, Tim; Sader, John E.: Global modes and nonlinear analysis of inverted-flag flapping (2018)
  16. Kressner, Daniel; Lu, Ding; Vandereycken, Bart: Subspace acceleration for the Crawford number and related eigenvalue optimization problems (2018)
  17. Laliena, Victor; Campo, Javier: An improved discretization of Schrödinger-like radial equations (2018)
  18. Lenders, Felix; Kirches, C.; Potschka, A.: trlib: a vector-free implementation of the GLTR method for iterative solution of the trust region problem (2018)
  19. Li, Huamin; Kluger, Yuval; Tygert, Mark: Randomized algorithms for distributed computation of principal component analysis and singular value decomposition (2018)
  20. Ma, Lingling; Jiang, Lijian: Convergence analysis for GMsFEM approximation of elliptic eigenvalue problems (2018)

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