Numerical stability

Numerical stability is the ability of a computer program to give the same answer no matter how many times it is calculated. It is important for computer programs to be stable because if a program gives different answers every time it is run, it will be very difficult to trust what it says. To make a program numerically stable, programmers have to make sure that small changes in the input data don't cause big changes in the output. For example, if a program was designed to calculate the average of three numbers, the program should always give the same result no matter what numbers are put in.