Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



An extrapolated Gauss-Seidel iteration for Hessenberg matrices

Author: L. J. Lardy
Journal: Math. Comp. 27 (1973), 921-926
MSC: Primary 65F10
MathSciNet review: 0327012
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that for certain systems of linear equations with coefficient matrices of Hessenberg form it is possible to use Gaussian elimination to obtain an extrapolated version of the Gauss-Seidel iterative process where the iteration matrix has spectral radius zero. Computational aspects of the procedure are discussed.

References [Enhancements On Off] (What's this?)

  • [1] F. W. Dorr, "An example of ill-conditioning in the numerical solution of singular perturbation problems," Math. Comp., v. 25, 1971, pp. 271-283. MR 0297142 (45:6200)
  • [2] E. Isaacson & H. B. Keller, Analysis of Numerical Methods, Wiley, New York, 1966. MR 34 #924. MR 0201039 (34:924)
  • [3] R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962. MR 28 #1725. MR 0158502 (28:1725)
  • [4] J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965. MR 32 #1894. MR 0184422 (32:1894)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65F10

Retrieve articles in all journals with MSC: 65F10

Additional Information

Keywords: Gaussian elimination, Gauss-Seidel iteration, Hessenberg matrices
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society