bisection method

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A numerical method for finding a root of an equation f(x)=0. If values a and b are found such that f(a) and f(b) have opposite signs and f is continuous on the interval [a, b], then (by the Intermediate Value Theorem) the equation has a root in (a, b). The method is to bisect the interval and replace it by either one half or the other, thereby closing in on the root.

Let c=Ɖ(a+b). Calculate f(c). If f(c) has the same sign as f(a), then take c as a new value for a; if not (so that f(c) has the same sign as f(b), take c as a new value for b. (If it should happen that f(c)=0, then c is a root and the aim of finding a root has been achieved.) Repeat this whole process until the length of the interval [a, b] is less than 2>, where > is specified in advance. The midpoint of the interval can then be taken as an approximation to the root, and the error will be less than >.

http://archives.math.utk.edu/visual.calculus/1/bisection.3/index.html An interactive page which demonstrates the method for finding a root of a cubic equation.

Subjects: Mathematics.

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