Condition Number

In numerical analysis, the condition number of a function measures how sensitive its output is to small changes, or errors, in its input, and so measures how much error can be expected to propagate through a calculation. It is formally the asymptotic worst case relative change in a functions output for a given relative change in its input. A problem with a low condition number is called well conditioned, since small input errors produce correspondingly small output errors, while an ill conditioned problem can produce large output changes from tiny input perturbations, making reliable solutions hard to obtain. As a practical rule of thumb, if a matrixs condition number is on the order of 10 to the k, roughly k digits of numerical accuracy may be lost beyond ordinary floating point precision limits, which makes the condition number a central concept in assessing the reliability of linear algebra computations.