Inverse iteration on defective matrices
Author:
Nai Fu Chen
Journal:
Math. Comp. 31 (1977), 726-732
MSC:
Primary 65F15
DOI:
https://doi.org/10.1090/S0025-5718-1977-0438682-6
MathSciNet review:
0438682
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Abstract | References | Similar Articles | Additional Information
Abstract: Very often, inverse iteration is used with shifts to accelerate convergence to an eigenvector. In this paper, it is shown that, if the eigenvalue belongs to a nonlinear elementary divisor, the vector sequences may diverge even when the shift sequences converge to the eigenvalue. The local behavior is discussed through a 
example, and a sufficient condition for the convergence of the vector sequence is given.
- [1] N. CHEN, The Rayleigh Quotient Iteration for Non-Normal Matrices, Ph. D. Dissertation, Electronic Research Laboratory Memorandum No. ERL-M548, University of California, Berkeley, 1975.
- [2] J. M. VARAH, The Computation of Bounds for the Invariant Subspaces of a General Matrix Operator, Ph. D. Dissertation, Stanford University, 1967.
- [3] J. H. Wilkinson, Inverse iteration in theory and in practice, Symposia Mathematica, Vol. X (Convegno di Analisi Numerica, INDAM, Rome, 1972) Academic Press, London, 1972, pp. 361–379. MR 0366017
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1977-0438682-6
Keywords:
Eigenvector,
eigenvalue,
nonlinear divisors,
convergence,
inverse iterations,
shifts
Article copyright:
© Copyright 1977
American Mathematical Society
