## Quick Reference

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.