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Numerische Mathematik

, Volume 31, Issue 1, pp 31–48 | Cite as

Rank-one modification of the symmetric eigenproblem

  • James R. Bunch
  • Christopher P. Nielsen
  • Danny C. Sorensen
Article

Summary

An algorithm is presented for computing the eigensystem of the rank-one modification of a symmetric matrix with known eigensystem. The explicit computation of the updated eigenvectors and the treatment of multiple eigenvalues are discussed. The sensitivity of the computed eigenvectors to errors in the updated eigenvalues is shown by a perturbation analysis.

Subject Classifications

AMS(MOS): 65F15 CR: 5.14 

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References

  1. 1.
    Bunch, J.R., Nielsen, C.P.: Updating the singular value decomposition. Numer. Math. (to appear)Google Scholar
  2. 2.
    Bunch, J.R., Rose, D.J.: Partitioning, tearing and modification of sparse linear systems. J. Math. Anal. Appl.48, 574–593 (1074)Google Scholar
  3. 3.
    Dennis, J.E., Moré, J.J.: Quasi-Newton methods, motivation and theory. SIAM Rev.19, 46–89 (1977)Google Scholar
  4. 4.
    Golub, G.H.: Some modified matrix eigenvalue problems. SIAM Rev.15, 318–334 (1973)Google Scholar
  5. 5.
    Stewart, G.W.: Introduction to matrix computations. New York: Academic Press 1973Google Scholar
  6. 6.
    Thompson, R.C.: The behavior of eigenvalues and singular values under perturbations of restricted rank. Linear Algebra and Appl.13, 69–78 (1976)Google Scholar
  7. 7.
    Wilkinson, J.H.: The algebraic eigenvalue problem. Oxford: Clarendon Press 1965Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • James R. Bunch
    • 1
  • Christopher P. Nielsen
    • 1
  • Danny C. Sorensen
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaSan Diego, La JollaUSA
  2. 2.Department of MathematicsUniversity of KentuckyLexingtonUSA

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