A New Variant of the Bisection Method
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12-29-2016, 04:56 PM
(This post was last modified: 12-30-2016 02:16 AM by Namir.)
Post: #1
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A New Variant of the Bisection Method
Encircling-Variant 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 = (Z-A)/2 Enjoy! Namir |
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