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Mathematics of Computation

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A generalization of the Jenkins-Traub method

Author: J. A. Ford
Journal: Math. Comp. 31 (1977), 193-203
MSC: Primary 65H05
MathSciNet review: 0428703
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Abstract: A class of methods for finding zeros of polynomials is derived which depends upon an arbitrary parameter $ \rho $. The Jenkins-Traub algorithm is a special case, corresponding to the choice $ \rho = \infty $. Global convergence is proved for large and small values of $ \rho $ and a duality between pairs of members is exhibited. Finally, we show that many members of the class (including the Jenkins-Traub method) converge with R-order at least 2.618..., which improves upon the result obtained by Jenkins and Traub [3].

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Article copyright: © Copyright 1977 American Mathematical Society