Talk:Condition number

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[edit] question about condition number

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)

I added a plausible derivation of the condition number for operator (induced) matrix norms. I hope it helps. Perdelsky 03:09, 5 August 2007 (UTC)

[edit] Relevance of precision

I am not sure if the relevance of finite/infinite precision is clear. If you have infinite precision, and do not assume any kind of errors in the input, the condition number is of no relevance. Berland 12:42, 18 January 2007 (UTC)

If you use exact arithmetic (infinite precision), and an iterative method to compute an approximation to your solution (whose rate of convergence degrades with increasing condition number), then the condition number is of great relevance. Lunch 17:38, 18 January 2007 (UTC)

You are absolutely right. I think these (subtle?) issues could/should be addressed in the article. Berland 21:22, 19 January 2007 (UTC)