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Lambert's Method

A root-finding algorithm also called Bailey's method and Hutton's method. For a function of the form g(x)=x^d-r, Lambert's method gives an iteration function

H_g(x)=((d-1)x^d+(d+1)r)/((d+1)x^d+(d-1)r)x,

so

x_(n+1)=x_n+H_g(x_n).

See also

Laguerre's Repeated Fraction, Root-Finding Algorithm

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References

Scavo, T. R. and Thoo, J. B. "On the Geometry of Halley's Method." Amer. Math. Monthly 102, 417-426, 1995.

Referenced on Wolfram|Alpha

Lambert's Method

Cite this as:

Weisstein, Eric W. "Lambert's Method." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LambertsMethod.html

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