programing 2

Root finding is a simple application of numerical methods. One method for root finding is called the Bisection method. Similar to the “zero” function in a typical TI-83 calculator, an interval is specified and the program searches for a root in that interval. If the function changes sign between the two bounds, a root exists in the interval. The value of the function is evaluated at the midpoint of the interval. Then the program checks to see if the sign of the function changes between the lower bound and the midpoint or the upper bound and the midpoint. The interval in which the sign changes becomes the new interval, effectively halving the interval size, and the process is repeated until the interval becomes small enough. Chapter 19 of the textbook explains the method in a more detailed manner.