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 564 articles , 1 standard article )

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  1. Aristoff, David; Bello-Rivas, Juan M.; Elber, Ron: A mathematical framework for exact milestoning (2016)
  2. Astudillo, R.; van Gijzen, M.B.: A restarted induced dimension reduction method to approximate eigenpairs of large unsymmetric matrices (2016)
  3. Bangerth, Wolfgang; Davydov, Denis; Heister, Timo; Heltai, Luca; Kanschat, Guido; Kronbichler, Martin; Maier, Matthias; Turcksin, Bruno; Wells, David: The deal.II library, version 8.4 (2016)
  4. Bonito, Andrea; Guermond, Jean-Luc; Luddens, Francky: An interior penalty method with $C^0$ finite elements for the approximation of the Maxwell equations in heterogeneous media: convergence analysis with minimal regularity (2016)
  5. Brown, Kirsty L.; Gejadze, Igor; Ramage, Alison: A multilevel approach for computing the limited-memory Hessian and its inverse in variational data assimilation (2016)
  6. Friedlander, Michael P.; Mac^edo, Ives: Low-rank spectral optimization via gauge duality (2016)
  7. Giani, Stefano; Grubišić, Luka; Międlar, Agnieszka; Ovall, Jeffrey S.: Robust error estimates for approximations of non-self-adjoint eigenvalue problems (2016)
  8. Guglielmi, Nicola: On the method by Rostami for computing the real stability radius of large and sparse matrices (2016)
  9. Guglielmi, Nicola; Manetta, Manuela: An iterative method for computing robustness of polynomial stability (2016)
  10. Huang, Tsung-Ming; Lin, Wen-Wei; Mehrmann, Volker: A Newton-type method with nonequivalence deflation for nonlinear eigenvalue problems arising in photonic crystal modeling (2016)
  11. Kalantzis, Vassilis; Li, Ruipeng; Saad, Yousef: Spectral Schur complement techniques for symmetric eigenvalue problems (2016)
  12. Kestyn, James; Polizzi, Eric; Tang, Ping Tak Peter: Feast eigensolver for non-Hermitian problems (2016)
  13. Lu, Ding; Su, Yangfeng; Bai, Zhaojun: Stability analysis of the two-level orthogonal Arnoldi procedure (2016)
  14. Saibaba, Arvind K.; Lee, Jonghyun; Kitanidis, Peter K.: Randomized algorithms for generalized Hermitian eigenvalue problems with application to computing Karhunen-Loève expansion. (2016)
  15. Schröder, Christian; Taslaman, Leo: Backward error analysis of the shift-and-invert Arnoldi algorithm (2016)
  16. Schweizer, Wolfgang: MATLAB compact (2016)
  17. Simoncini, V.: Computational methods for linear matrix equations (2016)
  18. Sirković, Petar; Kressner, Daniel: Subspace acceleration for large-scale parameter-dependent Hermitian eigenproblems (2016)
  19. Solonen, Antti; Cui, Tiangang; Hakkarainen, Janne; Marzouk, Youssef: On dimension reduction in Gaussian filters (2016)
  20. Sorensen, D.C.; Embree, Mark: A DEIM induced CUR factorization (2016)

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