Gauss–Legendre algorithm: Difference between revisions

Revision as of 02:21, 11 October 2022

Revision as of 19:30, 20 February 2023

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== Algorithm ==

#

# Initial value setting: <math display="block">a_0 = 1\qquad b_0 = \frac{1}{\sqrt{2}}\qquad t_0 = \frac{1}{4}\qquad p_0 = 1.</math>

# Repeat the following instructions until the difference of <math>a_n</math> and <math>b_n</math> is within the desired accuracy: <math display="block"> \begin{align}

a_{n+1} & = \frac{a_n + b_n}{2}, \\

\\

b_{n+1} & = \sqrt{a_n b_n}, \\

\\

t_{n+1} & = t_n - p_n(a_{n}-a_{n+1})^2, \\

\\