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Mathematics of Computation

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



Divided differences, shift transformations and Larkin's root finding method

Authors: A. Neumaier and A. Schäfer
Journal: Math. Comp. 45 (1985), 181-196
MSC: Primary 65H05
MathSciNet review: 790651
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Abstract: For a one-dimensional complex-valued function f this paper deals with iterative root finding methods using divided differences of f. Assuming that f is given in a Newtonian representation we show how Horner-like transformations ("shift transformations") yield the divided differences needed in each iteration step. In particular, we consider an iteration method given by Larkin [5] and derive an equivalent version of this method fitting into this context. Monotonic convergence to real roots of real polynomials is investigated. Both "shift-" and "nonshift versions" of several root finding methods are tested and compared with respect to their numerical behavior.

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Article copyright: © Copyright 1985 American Mathematical Society

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