Algorithm 827: irbleigs: A MATLAB program for computing a few eigenpairs of a large sparse Hermitian matrix. irbleigs is a MATLAB program for computing a few eigenvalues and associated eigenvectors of a sparse Hermitian matrix of large order n. The matrix is accessed only through the evaluation of matrix-vector products. Working space of only a few n-vectors is required. The program implements a restarted block-Lanczos method. Judicious choices of acceleration polynomials make it possible to compute approximations of a few of the largest eigenvalues, a few of the smallest eigenvalues, or a few eigenvalues in the vicinity of a user-specified point on the real axis. irbleigs also can be applied to certain large generalized eigenproblems as well as to the computation of a few nearby singular values and associated right and left singular vectors of a large general matrix.

References in zbMATH (referenced in 14 articles , 2 standard articles )

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  1. Li, Ruipeng; Xi, Yuanzhe; Vecharynski, Eugene; Yang, Chao; Saad, Yousef: A thick-restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems (2016)
  2. Fenu, C.; Martin, D.; Reichel, L.; Rodriguez, G.: Network analysis via partial spectral factorization and Gauss quadrature (2013)
  3. Wang, Xiang; Lu, Lin-zhang; Niu, Qiang; Nie, Yong-ming: A refined variant of the inverse-free Krylov subspace method for symmetric generalized eigenvalue problems (2013)
  4. Niu, Qiang; Lu, Linzhang: Deflated block Krylov subspace methods for large scale eigenvalue problems (2010)
  5. Stathopoulos, Andreas; McCombs, James R.: PRIMME: preconditioned iterative multimethod eigensolver -- methods and software description (2010)
  6. Zhou, Yunkai: A block Chebyshev-Davidson method with inner-outer restart for large eigenvalue problems (2010)
  7. Baglama, James: Augmented block Householder Arnoldi method (2008)
  8. Zhou, Yunkai; Saad, Yousef: Block Krylov-Schur method for large symmetric eigenvalue problems (2008)
  9. Habib, H.M.; El-Zahar, E.R.: An algorithm for solving singular perturbation problems with mechanization (2007)
  10. Zhou, Yunkai; Saad, Yousef: A Chebyshev-Davidson algorithm for large symmetric eigenproblems (2007)
  11. Bunse-Gerstner, Angelika; Guerra-Ones, Valia; De La Vega, Humberto Madrid: An improved preconditioned LSQR for discrete ill-posed problems (2006)
  12. Baglama, James; Reichel, Lothar: Augmented implicitly restarted Lanczos bidiagonalization methods (2005)
  13. Baglama, J.; Calvetti, D.; Reichel, L.: IRBL: An implicitly restarted Block-Lanczos method for large-scale Hermitian eigenproblems (2003)
  14. Baglama, J.; Calvetti, D.; Reichel, L.: Algorithm 827: irbleigs: A MATLAB program for computing a few eigenpairs of a large sparse Hermitian matrix (2003)