Talk:Condition number

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I'll move this to the reference desk in a day or two if someone isn't watching here.

Can someone help me with an estimate of how big a condition number actually has to be before a matrix is considered "ill conditioned?" I'm sure it's dependent on many things but I'd like to get a grasp on it.

I'm trying to show that in a bunch of cases (200 or so) two 2D vectors are "approximately" multiples of one another. So I make a 2x2 matrix out of these two vectors, and I find the condition number. On average the condition number is around 2e6, and the minimum is 9e4. Does this make the vectors approximately multiples of one another? moink 16:58, 7 Apr 2004 (UTC)

The error in the approximate solution is no greater than the (condition number) x (relative error in the initial solution). If the new approximate solution is not within the desired precision of the actual solution, then the system would be "ill-conditioned." Also, to obtain a higher precision in an ill-conditioned system, a much more accurate initial condition is required.Jaboles 20:49, 23 August 2006 (UTC)

[edit] Confusing

"wheras a large condition number will enhance error in b." I think this is confusing because we are talking about the bad conditioning increasing the amount of error in the calculated x due do a small error in b (and not really doing anything to b). Richard Giuly 08:53, 1 November 2006 (UTC)

I agree. The next step is that you think of a better formulation and edit the article. These articles don't write themselves ;) Don't worry too much about making mistakes; they will be corrected. -- Jitse Niesen (talk) 10:44, 1 November 2006 (UTC)

I tried to change it myself. -- Jitse Niesen (talk) 11:20, 8 November 2006 (UTC)