Sidi's generalized secant method: Difference between revisions

Revision as of 12:38, 16 March 2013

Revision as of 13:25, 16 March 2013

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:<math> \lim\limits_{n \to \infty} \frac{|x_{n+1}|}{|x_n|^{\psi_k}} = \mu </math>

with a [[rate of convergence]] <math>\mu</math> > 0. The order of convergence <math>\psi_k</math>. is the [[Descartes's rule of signs|only positive root]] of the polynomial

:<math> s^{k+1} - s^k - s^{k-1} - \dots - s - 1 </math>

We have e.g. <math>\psi_1 = (1+\sqrt{5})/2</math> ≈ 1.6180, <math>\psi_2</math> ≈ 1.8393 and <math>\psi_3</math> ≈ 1.9276.

== Related algorithms ==