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Topic: Matrix inversion - linear algebra - higher accuracy for some matrix
rows ? (Tikhonov regularization???)

Replies: 6   Last Post: Sep 11, 2012 12:49 PM

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Matt J

Posts: 4,997
Registered: 11/28/09
Re: Matrix inversion - linear algebra - higher accuracy for some matrix
Posted: Sep 10, 2012 4:19 PM
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someone <> wrote in message <k2lgj3$s1a$>...
> Here's the deal:
> A-matrix is approx. 90x90, mostly diagonal but also quite some
> offdiagonal elements here and there.
> Some rows in the matrix are equations that is harder to satisfy than
> others because something is rotating at different speeds - it means that
> those matrix equations (the lower rows in A) that has a physical
> connection to something that rotates really fast, causes some severe
> oscillations (it gives oscillating accelerations and wrong forces)
> because the timestep is very high compared to the rotation speed for the
> last rows in A... Got it?
> Ok, is there any way to make: x = A\b more accurate for the lower
> rows/equations or ???


You could put lower weights on the problematic rows


where W is a diagonal weighting matrix. Or you could throw away those rows altogether and try PINV. Throwing away the bad rows and adding regularization would be even better, but it's not clear to me, from the physics of your problem, what regularization would be appropriate.

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