A generalization of the Jenkins-Traub method

Author:
J. A. Ford

Journal:
Math. Comp. **31** (1977), 193-203

MSC:
Primary 65H05

DOI:
https://doi.org/10.1090/S0025-5718-1977-0428703-9

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 . The Jenkins-Traub algorithm is a special case, corresponding to the choice . Global convergence is proved for large and small values of 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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DOI:
https://doi.org/10.1090/S0025-5718-1977-0428703-9

Article copyright:
© Copyright 1977
American Mathematical Society