Content deleted Content added
Added free to read link in citations with OAbot #oabot |
m Gander(1978) → Gander (1978) |
||
Line 11:
:<math>x_{n+1}=x_{n}-\frac{f(x_n)}{f'(x_n)} \left({\frac{1}{1-\frac{f(x_n)f''(x_n)}{2(f'(x_n))^2}}}\right).</math>
This is referred to as Halley's formula.
This ''geometrical interpretation'' <math>h(z)</math> was derived by Gander (1978), where the equivalent iteration also was derived by applying Newton's method to
:<math>g(x)=\frac{f(x)}{\sqrt{f'(x)}}=0.</math>
We call this ''algebraic interpretation'' <math>g(x)</math> of Halley's formula.
Line 27:
SRA strictly implies this one-point second-order interpolation by a simple rational function.
We can notice that even third order method is a variation of Newton's method. We see the Newton's steps are multiplied by some factors. These factors are called the ''convergence factors'' of the variations, which are useful for analyzing the rate of convergence. See Gander (1978).
== References ==
| |||