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condition number

A single number estimating how much a problem magnifies a small relative error in its input into a relative error in its output.

A problem's condition number approximates the ratio of the relative change in output to the relative change in input that caused it; a condition number near 1 signals a well-conditioned problem, and a very large one signals an ill-conditioned problem.

Examples

  • A condition number of 10^6 means a 10^{-8} relative input error can become as large as a 10^{-2} relative error in the output.

See also

conditioning
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