论文信息 - On the global convergence of Halley's iteration formula

On the global convergence of Halley's iteration formula

A point-iterative process similar to, but structurally simpler than, Ostrowski's square root technique is examined. This process is shown to be globally convergent monotonically to the zeros of entire functions of genus 0 and 1 (and in certain cases of genus 2) which are real for real arguments and have only real zeros.

B. Dawson | M. Davies

[1] E. Bodewig,et al. On types of convergence and on the behavior of approximations in the neighborhood of a multiple root of an equation , 1949 .

[2] A. Ostrowski. Solution of equations in Euclidean and Banach spaces , 1973 .