Algorithm 776: SRRIT: A Fortran subroutine to calculate the dominant invariant subspace of a nonsymmetric matrix SRRIT is a Fortran program to calculate an approximate orthonormal basis for a dominant invariant subspace of a real matrix A by the method of simultaneous iteration. Specifically, given an integer m, SRRIT computes a matrix Q with m orthonormal columns and real quasi-triangular matrix T of order m such that the equation AQ=QT is satisfied up to a tolerance specified by the user. The eigenvalues of T are approximations to the m eigenvalues of largest absolute magnitude of A, and the columns of Q span the invariant subspace corresponding to those eigenvalues. SRRIT references A only through a user-provided subroutine to form the product AQ; hence it is suitable for large sparse problems.

References in zbMATH (referenced in 26 articles , 1 standard article )

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  1. Saad, Yousef: Numerical methods for large eigenvalue problems (2011)
  2. Zhao, Shan: A fourth order finite difference method for waveguides with curved perfectly conducting boundaries (2010)
  3. Zhao, Shan: High order matched interface and boundary methods for the Helmholtz equation in media with arbitrarily curved interfaces (2010)
  4. Theodoropoulos, C.; Luna-Ortiz, E.: A reduced input/output dynamic optimisation method for macroscopic and microscopic systems (2006)
  5. Luna-Ortiz, Eduardo; Theodoropoulos, Constantinos: An input/output model reduction-based optimization scheme for large-scale systems (2005)
  6. Zemke, Jens-Peter Max: Krylov subspace methods in finite precision: A unified approach (2003)
  7. Lehoucq, R.B.: Implicitly restarted Arnoldi methods and subspace iteration (2001)
  8. Bai, Zhaojun (ed.); Demmel, James (ed.); Dongarra, Jack (ed.); Ruhe, Axel (ed.); Van der Vorst, Henk (ed.): Templates for the solution of algebraic eigenvalue problems. A practical guide (2000)
  9. Golub, Gene H.; van der Vorst, Henk A.: Eigenvalue computation in the 20th century (2000)
  10. Kågström, Bo; Wiberg, Petter: Extracting partial canonical structure for large scale eigenvalue problems (2000)
  11. Bai, Zhaojun; Day, David; Ye, Qiang: ABLE: An adaptive block Lanczos method for non-Hermitian eigenvalue problems (1999)
  12. Sorensen, D.C.; Yang, C.: A truncated RQ iteration for large scale eigenvalue calculations (1998)
  13. Bai, Z.; Stewart, G.W.: Algorithm 776: SRRIT: A Fortran subroutine to calculate the dominant invariant subspace of a nonsymmetric matrix (1997)
  14. Sorensen, Danny C.: Implicitly restarted Arnoldi/Lanczos methods for large scale eigenvalue calculations (1997)
  15. van der Vorst, Henk A.; Golub, Gene H.: 150 years old and still alive: Eigenproblems (1997)
  16. Lehoucq, R.B.; Sorensen, D.C.: Deflation techniques for an implicitly restarted Arnoldi iteration (1996)
  17. Duff, I.S.; Scott, J.A.: Corrigendum: Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration (1995)
  18. Scott, J.A.: An Arnoldi code for computing selected eigenvalues of sparse, real unsymmetric matrices (1995)
  19. Achar, N.S.; Gaonkar, G.H.: An exploratory study of a subspace iteration method as an alternative to the QR method for Floquet eigenanalysis (1994)
  20. Bai, Zhaojun: Error analysis of the Lanczos algorithm for the nonsymmetric eigenvalue problem (1994)

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