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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Root-finding by fitting rational functions


Author: F. M. Larkin
Journal: Math. Comp. 35 (1980), 803-816
MSC: Primary 65H05
MathSciNet review: 572858
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Abstract | References | Similar Articles | Additional Information

Abstract: A tabular, recursive method is presented for the computation of a sequence of abscissae designed to converge to a simple zero of an analytic function. The key to the method is an efficient means for evaluating the zeros of a sequence of rational functions, having linear numerators, fitted to information previously computed.

Regional and asymptotic convergence properties of the method are described. Conditions sufficient to ensure convergence are derived, and it is shown that asymptotically quadratic convergence can be achieved, at the cost of only a moderate amount of "overhead" computation.


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

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1980-0572858-2
PII: S 0025-5718(1980)0572858-2
Article copyright: © Copyright 1980 American Mathematical Society