Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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].


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


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65H05

Retrieve articles in all journals with MSC: 65H05


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1977-0428703-9
Article copyright: © Copyright 1977 American Mathematical Society