
Re: Matrix inversion  linear algebra  higher accuracy for some matrix
Posted:
Sep 11, 2012 2:09 AM


On 09/10/2012 10:19 PM, Matt J wrote: > someone <newsboost@gmail.com> wrote in message > <k2lgj3$s1a$1@dontemail.me>... >> Here's the deal: >> >> Amatrix 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 > > x=(W*A)\(W*b) > > where W is a diagonal weighting matrix. Or you could throw away those
Thanks, Matt... Wow, thanks... I didn't even knew you could do that... So for instance I make W ones in the top half and maybe 100 in the lowest half ?
> 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.
I think I only know tikhonov from a few years ago... Maybe I also tried another option at that time, cannot really remember. Anyone can cast light on this ?
The problem is that I cannot just throw away bad rows  I also need to calculate the value (accelerations etc) of slowly rotating objects... I would be nice if I can only apply regularization to the lowest equations (lowest part of the Amatrix  this is where I have high velocities)...
Anyway  if someone knows anything, can cast light on this, please post your comments !

