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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: 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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Article copyright: © Copyright 1980 American Mathematical Society

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