G.W. Stewart pp 521-631 | Cite as

Papers on the SVD, Eigenproblem and Invariant Subspaces: Algorithms

Part of the Contemporary Mathematicians book series (CM)


Invariant Subspace Rayleigh Quotient Block Diagonalization Singular Subspace Hessenberg Matrix 
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  1. 1.
    Bauer, F. L.: Das Verfahren der Treppeniteration und verwandte Verfahren zur Lösung algebraischer Eigenwertprobleme. Z. Angew. Math. Phys. 8, 214–235 (1957).MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Householder, A. S.: The theory of matrices in numerical analysis. New York: Blaisdell Publishing Co. 1964.MATHGoogle Scholar
  3. 3.
    Swanson, C. A.: An inequality for linear transformations with eigenvalues. Bull. Amer. Math. Soc. 67, 607–608 (1961).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Wilkinson, J. H.: Convergence of the LR, QR, and related algorithms. Comp. J. 8, 77–84 (1965).MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    The algebraic eigenvalue problem. Oxford: Clarendon Press 1965.Google Scholar
  6. [1]
    R. Bhatia, L. Elsner, and G. Krause, Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix, Linear Algebra and Its Applications 142 (1990), 195–209. MR 92i:12001MathSciNetCrossRefMATHGoogle Scholar
  7. [2]
    L. Elsner, An optimal bound for the spectral variation of two matrices, Linear Algebra and Its Applications 71 (1985), 77–80. MR 87c:15035MathSciNetCrossRefMATHGoogle Scholar
  8. [3]
    G. H. Golub and C. F. Van Loan, Matrix computations, second ed., Johns Hopkins University Press, Baltimore, MD, 1989. MR 90d:65055MATHGoogle Scholar
  9. [4]
    I. C. F. Ipsen, Absolute and relative perturbation bounds for invariant subspaces of matrices, Technical Report TR9735, Center for Research in Scientific Computation, Mathematics Department, North Carolina State University, 1998.Google Scholar
  10. [5]
    Z. Jia, Some numerical methods for large unsymmetric eigenproblems, Ph.D. thesis, University of Bielefeld, 1994.Google Scholar
  11. [6]
    ——, The convergence of generalized Lanczos methods for large unsymmetric eigenproblems, SIAM Journal on Matrix Analysis and Applications 16 (1995), 843862. MR 96d:65062Google Scholar
  12. [7]
    ——, Refined iterative algorithm based on Arnoldi’s process for large unsymmetric eigenproblems, Linear Algebra and Its Applications 259 (1997), 123. MR 98c:65060Google Scholar
  13. [8]
    ——, Generalized block Lanczos methods for large unsymmetric eigenproblems, Numerische Mathematik 80 (1998), 171189. MR 95f:65059Google Scholar
  14. [9]
    ——, A refined iterative algorithm based on the block Arnoldi algorithm, Linear Algebra and Its Applications 270 (1998), 171189. MR 98m:65055Google Scholar
  15. [10]
    ——, Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm, Linear Algebra and Its Applications 287 (1999), 191214. MR 99j:65046Google Scholar
  16. [11]
    ——, A refined subspace iteration algorithm for large sparse eigenproblems, To appear in Applied Numerical Mathematics., 1999.Google Scholar
  17. [12]
    Y. Saad, Numerical methods for large eigenvalue problems: Theory and algorithms, John Wiley, New York, 1992. MR 93h:65052MATHGoogle Scholar
  18. [13]
    G. L. G. Sleijpen and H. A. Van der Vorst, A Jacobi Davidson iteration method for linear eigenvalue problems, SIAM Journal on Matrix Analysis and Applications 17 (1996), 401–425. MR 96m:65042MathSciNetCrossRefMATHGoogle Scholar
  19. [14]
    G. W. Stewart and J.-G. Sun, Matrix perturbation theory, Academic Press, New York, 1990. MR 92a:65017MATHGoogle Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsTufts UniversityMedfordUSA
  2. 2.Computer Science Department and Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA

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