Numerical stability

The numerical stability of a method measures the difference between the result of a numerical problem and it's computational approximation.

The numerical stability of a method together with the condition number defines how good a result we can get when using approximate methods to calculate the results of a mathematical problem.

When solving a numerical problem most of the time one normally resorts to an approximated method to calculate a result. Two types of errors can occur:

• Cutoff errors: One can only make a finite number of calculations. Examples: calculating a transcendental function using it's Taylor expansion, integrating using a sum of finite rectangles.
• Roundoff errors: Certain numbers need an infinite number of digits to be represented (pi), when rounding these numbers the roudoff errors will propagate through the calculation.