A New Variant of the Bisection Method

12292016, 04:56 PM
(This post was last modified: 12302016 02:16 AM by Namir.)
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A New Variant of the Bisection Method
EncirclingVariant of Bisection
This algorithm is inspired by the Bisection method. It requires, in general, fewer iterations than the Bisection. The basic idea is to start with x=A, such that A<Xroot, and march towards the root. As the value of A passes over the root, we change the sign of the marching step and also reduce it. This change makes the value of A move around the root and closes in on it. Given a function f(x)=0 and x=A, such that A<Xroot, and the root bracketing interval [A,Z], and the tolerance Toler. The value of Z is needed only to calculate the initial search step. You can eliminate Z if you provide the value for the initial search step. Removing the nested IF statement causes the algorithm to slow down and require significantly more iterations than the Bisection method. Code: Delta = (ZA)/2 Enjoy! Namir 

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A New Variant of the Bisection Method  Namir  12292016 04:56 PM

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