Iteration consists of repeating an operation of a value obtained by the same operation. It is often used in making successive approximations, each one more accurate than the one that preceded it. One begins with an approximate solution and substitutes it into an appropriate formula to obtain a better approximation. This approximation is subsequently substituted into the same formula to arrive at a still better approximation, and so on, until an exact solution or one that is arbitrarily close to an exact solution is obtained.

An example of using iteration for approximation is finding the square root. If s is the exact square root of A, then A |6-8| s = s. For example, since 8 is the square root of 64, it is true that 64 |6-8| 8 = 8. If you did not know the value of |5-14| 64, you might guess 7 as the value. By dividing 64 by 7, you get 9.1. The average of 7 and...