Matrix Algebra pp 307-325 | Cite as

Evaluation of Eigenvalues and Eigenvectors

  • James E. Gentle
Part of the Springer Texts in Statistics book series (STS)


Before we discuss methods for computing eigenvalues, we recall a remark made in Chap.  5 A given nth-degree polynomial p(c) is the characteristic polynomial of some matrix. The companion matrix of equation ( 3.225) is one such matrix.


  1. Benzi, Michele. 2002. Preconditioning techniques for large linear systems: A survey. Journal of Computational Physics 182:418–477.MathSciNetCrossRefzbMATHGoogle Scholar
  2. Chan, T. F. 1982a. An improved algorithm for computing the singular value decomposition. ACM Transactions on Mathematical Software 8:72–83.Google Scholar
  3. Chan, T. F. 1982b. Algorithm 581: An improved algorithm for computing the singular value decomposition. ACM Transactions on Mathematical Software 8:84–88.Google Scholar
  4. Golub, G., and W. Kahan. 1965. Calculating the singular values and pseudo-inverse of a matrix. SIAM Journal of Numerical Analysis, Series B 2:205–224.MathSciNetzbMATHGoogle Scholar
  5. Golub, G. H., and C. Reinsch. 1970. Singular value decomposition and least squares solutions. Numerische Mathematik 14:403–420.MathSciNetCrossRefzbMATHGoogle Scholar
  6. Golub, Gene H., and Charles F. Van Loan. 1996. Matrix Computations, 3rd ed. Baltimore: The Johns Hopkins Press.zbMATHGoogle Scholar
  7. Haag, J. B., and D. S. Watkins. 1993. QR-like algorithms for the nonsymmetric eigenvalue problem. ACM Transactions on Mathematical Software 19:407–418.CrossRefzbMATHGoogle Scholar
  8. Luk, F. T., and H. Park. 1989. On parallel Jacobi orderings. SIAM Journal on Scientific and Statistical Computing 10:18–26.MathSciNetCrossRefzbMATHGoogle Scholar
  9. Trefethen, Lloyd N., and David Bau III. 1997. Numerical Linear Algebra. Philadelphia: Society for Industrial and Applied Mathematics.CrossRefzbMATHGoogle Scholar
  10. Watkins, David S. 2002. Fundamentals of Matrix Computations, 2nd ed. New York: John Wiley and Sons.CrossRefzbMATHGoogle Scholar
  11. Zhou, Bing Bing, and Richard P. Brent. 2003. An efficient method for computing eigenvalues of a real normal matrix. Journal of Parallel and Distributed Computing 63:638–648.CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • James E. Gentle
    • 1
  1. 1.FairfaxUSA

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