A generalization of the Jenkins-Traub method

Ford, J. A.

doi:10.1090/S0025-5718-1977-0428703-9

A generalization of the Jenkins-Traub method
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by J. A. Ford PDF

Math. Comp. 31 (1977), 193-203 Request permission

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

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