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Muller's Method

Generalizes the secant method of root finding by using quadratic 3-point interpolation

q=(x_n-x_(n-1))/(x_(n-1)-x_(n-2)).
(1)

Then define

A=qP(x_n)-q(1+q)P(x_(n-1))+q^2P(x_(n-2))
(2)
B=(2q+1)P(x_n)-(1+q)^2P(x_(n-1))+q^2P(x_(n-2))
(3)
C=(1+q)P(x_n),
(4)

and the next iteration is

x_(n+1)=x_n-(x_n-x_(n-1))(2C)/(max(B+/-sqrt(B^2-4AC))).
(5)

This method can also be used to find complex zeros of analytic functions.

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References

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, p. 364, 1992.

Referenced on Wolfram|Alpha

Muller's Method

Cite this as:

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

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