11-05-2008, 10:40 AM | #1 | ||
College Starter
Join Date: Oct 2000
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math problem: fuzzy system of linear equations
i've got a math problem and am struggling with coming up with an answer. i have a system of linear equations like:
ax + by + cz = 123456... dx + ey + fz = 7890123... gx + hy + iz = 456789... (In my case, instead of a 3 x 3 matrix like the one above, it's an 8 by 8 matrix.) 8 equations, 8 unknowns. I know that if the 8 equations are "consistent", then an exact solution could be determined using linear algebra row reduction, Cramer's rule, or similar techniques. BUt my problem is that the 8 equations are known to be inconsistent. In other words, ax+by+cz doesn't exactly equal 123456, but rather 123456 is some apprximation with an unknown accuracy. I don't expect or want an exact answer to the 8 unknowns, but rather a range of values, or a statistical probability of answers. Any thoughts?
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11-05-2008, 11:36 AM | #2 |
Pro Starter
Join Date: Oct 2000
Location: Cary, NC
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Matlab? Maple? Mathcad?
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-- Greg -- Author of various FOF utilities |
11-05-2008, 11:39 AM | #3 |
College Benchwarmer
Join Date: Oct 2002
Location: Edmonton, AB
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Nothing to add, I'll move along.
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11-05-2008, 11:44 AM | #4 |
Grizzled Veteran
Join Date: Oct 2000
Location: Stuck in Yinzerville, PA
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Do you know how much the approximate values range?
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11-05-2008, 12:02 PM | #5 |
College Prospect
Join Date: May 2005
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I think you would want to use Maximum likelihood estimation.
Maximum likelihood - Wikipedia, the free encyclopedia |
11-05-2008, 12:24 PM | #6 | |
College Starter
Join Date: Oct 2000
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Quote:
thanks - i think this might be what i'm looking for (now i just need a couple years of advanced statistics training)
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11-05-2008, 12:26 PM | #7 |
Pro Starter
Join Date: Jan 2001
Location: Burke, VA
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Maximum Likelihood - snicker....
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11-05-2008, 12:59 PM | #8 |
H.S. Freshman Team
Join Date: Dec 2007
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if you have matlab or one of the free knockoffs, look up SVD (Singular Value Decomposition), this gives you a best estimation of the 8 unknown. Note: you can also feed it 8+ equations to give you best guess on the 8 unknowns
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