Mediterranean Journal of Mathematics

, Volume 12, Issue 2, pp 555–572

# On the Convergence of Halley’s Method for Multiple Polynomial Zeros

• Petko D. Proinov
• Stoil I. Ivanov
Article

## Abstract

In this paper, we investigate the local convergence of Halley’s method for the computation of a multiple polynomial zero with known multiplicity. We establish two local convergence theorems for Halley’s method for multiple polynomial zeros under different initial conditions. The convergence of these results is cubic right from the first iteration. Also we find an initial condition which guarantees that an initial guess is an approximate zero of the second kind for Halley’s method. All of the results are new even in the case of simple zeros.

## Mathematics Subject Classification (2010)

Primary 65H04 Secondary 12Y05

## Keywords

Halley’s method polynomial zeros multiple zeros local convergence error estimates

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