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Re: Matrix inversion - linear algebra - higher accuracy for some matrix rows ? (Tikhonov regularization???)
Posted:
Sep 11, 2012 11:07 AM
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"someone" <newsboost@gmail.com> wrote in message
news:k2lgj3$s1a$1@dont-email.me...
> 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 ???
>
>
> Another possibility I've been thinking about - in order to avoid these
> oscillations I talked about before - is to use regularization, maybe? I
> did a project some years ago using Tikhonov regularization, but here
> AFAIR - the idea was that all the elements in the solution-vector x could
> not change too much... This will allow me to use higher timesteps and
> avoid the oscillations... Understand it ?
>
>
> ELABORATION FOR THOSE WHO DON'T UNDERSTAND THE PHYSICS:
> Here's an elaboration of why I have a problem with high angular
> velocities: If some part of the problem (top rows in A) rotates very slow,
> i.e. at 1 rad/s and your timestep is 0.01 sec - it means that you have 100
> timesteps per rotation. That's ok... However, the lower rows in A rotates
> much faster - then I only get maybe 5-8 timesteps per rotation. This gives
> some VERY annoying oscillations and forces going in "random" directions
> because the motion is not smoothly captured.
>
> I want my program to solve x = A\b quickly and efficent - any ideas that
> might help me (and keep the computation time reasonable) ? Any tricks /
> tips ?
>
> I really hope to hear from some clever experts here... Thanks...
You might try lscov: http://www.mathworks.com/help/techdoc/ref/lscov.html
It will allow you to weight the observations.
--
Loren
http://blogs.mathworks.com/loren/
http://www.mathworks.com/matlabcentral/
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