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Unformatted text preview: Condition Numbers A problem is well conditioned if a small change in the input always creates a small change in the output (solution). A problem is ill-conditioned if a small change in the input can create a large change in the solution (output). There is actually a continuum here, ranging from the extremely well conditioned (e.g. evaluate the fcn f ( x ) = 1) to the extremely ill-conditioned, (e.g. evaluate a fcn at a discontinuity, infinitely ill-conditioned problems are often called ill-posed). In order to quantify the notion, we will define a condition number . A condition number is simply a number which describes how well or ill-conditioned a problem is; the bigger the number the more ill-conditioned the problem. Ideally, an absolute condition number, , will behave as follows: k change in solution k = k change in input k , or a relative condition number, , would satisfy k change in solution k k solution k = k change in input k k input k ....
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- Fall '10