Asymptotic behavior of vector recurrences with applications

Authors:
Alan Feldstein and J. F. Traub

Journal:
Math. Comp. **31** (1977), 180-192

MSC:
Primary 65Q05

DOI:
https://doi.org/10.1090/S0025-5718-1977-0426464-0

MathSciNet review:
0426464

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Abstract | References | Similar Articles | Additional Information

Abstract: The behavior of the vector recurrence is studied under very weak assumptions. Let denote the spectral radius of *M* and let . Then if the are bounded in norm and a certain subspace hypothesis holds, the root order of the is shown to be . If one additional hypothesis on the dimension of the principal Jordan blocks of *M* holds, then the quotient order of the is also . The behavior of the homogeneous recurrence is studied for all values of .

These results are applied to the analysis of

(1) Nonlinear iteration with application to iteration with memory and to parallel iteration algorithms.

(2) Order and efficiency of composite iteration.

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DOI:
https://doi.org/10.1090/S0025-5718-1977-0426464-0

Article copyright:
© Copyright 1977
American Mathematical Society