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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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Posts: 74
Registered: 4/30/08
Re: Matrix inversion - linear algebra - higher accuracy for some
Posted: Sep 11, 2012 12:25 PM
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On 2012-09-11 16:18, Matt J wrote:> someone <newsboost@gmail.com> wrote
in message
> <k2mkjl$nla$1@dont-email.me>...
>> 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 ?

> ======================
> You would want to put the larger weights on the good equations, not the
> bad ones.

Hmm. Ok, makes sense... I must try that some time, but maybe not now...

Thanks - I just realize that I think my problem is due to a coarse
timestep which gives problems with the time-integration, see below...

>> The problem is that I cannot just throw away bad rows
> ================
> Why not? If they contain bad information, of what benefit are they?

I think initially in each timestep, they contain "correct" information.

However, when I integrate the solution (I do that with ODE45) from this
matrix then I get position and velocities. BUT if I don't have a small
timestep (smooth movements) then I integrate something that moves
"randomly" because if something rotates at maybe 100 rad/s but the
timestep only allows for maybe 5 steps per rotation, then the
accelerations will seem to go in "arbitrary" directions, causing
oscillations... The integrated solution (position and velocities) from
previous steps is used in the next step so the error grows with time.
But if the accelerations are wrong (due to big oscillations), then
things will move and have a wrong position. Then everything becomes more
and more wrong with time... This is my problem...

hmmmm.... If that is the case, then I must correct myself because then
my question is wrong... Maybe, if I one day get really clever, I might
be able to formulate my problem such that I don't have this problem. I
bet that for a clever guy, this problem can be formulated in a way so I
don't need so small timesteps (it's just an object that rotates and
doesn't move, connected to some other objects that reacts to some forces
and move a bit)...

Maybe I should just forget about this - if we should go into the physics
for such a big matrix and all my equations, that would take too long time...

I hope you understand that my rows are not "bad" as in "throw them away
and just ignore-them"-bad... More "bad" as in "damnit, if I was clever,
I should make a correction on the RHS of the equation so this stupid
program doesn't oscillate for a normal timestep-size"...

For small timesteps, the oscillations go towards zero... I BET, there's
a clever solution. However, without going into the physics, I guess I'll
not come any close now. I think the problem is formulated in a bad way
in the first place so I need a small timestep...

I thought maybe regularization or something clever other than that could
help (to avoid these STUPID oscillations for a normal timestep-size),
for just these problematic "rows" in the A-matrix... Now I'm not so
sure... hmm...

Thanks for your comments...

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