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→One-point third-order iterative method: Halley's formula: clear notations |
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:<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.
==One-point second-order iterative method: Simple rational approximation==
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