In the field of numerical analysis, the condition number of a function with respect to an argument measures the asymptotically worst case of how much the function can change in proportion to small changes in the argument. The "function" is the solution of a problem and the "arguments" are the data in the problem.
A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned.
The condition number is a property of the problem. Paired with the problem are any number of algorithms that can be used to solve the problem, that is, to calculate the solution. Some algorithms have a property called backward stability. In general, a backward stable algorithm can be expected to accurately solve well-conditioned problems. Numerical analysis textbooks give formulas for the condition numbers of problems and identify the backward stable algorithms.
As a general rule of thumb, if the condition number, then you may lose up to digits of accuracy on top of what would be lost to the numerical method due to loss of precision from arithmetic methods. However, the condition number does not give the exact value of the maximum inaccuracy that may occur in the algorithm. It generally just bounds it with an estimate (whose computed value depends on the choice of the norm to measure the inaccuracy).
Read more about Condition Number: Matrices, Other Contexts
Famous quotes containing the words condition and/or number:
“Virginity is now a mere preamble or waiting room to be got out of as soon as possible; it is without significance. Old age is similarly a waiting room, where you go after life’s over and wait for cancer or a stroke. The years before and after the menstrual years are vestigial: the only meaningful condition left to women is that of fruitfulness.”
—Ursula K. Le Guin (b. 1929)
“God ... created a number of possibilities in case some of his prototypes failed—that is the meaning of evolution.”
—Graham Greene (1904–1991)