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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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text-dude

Posts: 74
Registered: 4/30/08
Re: Matrix inversion - linear algebra - higher accuracy for some
matrix

Posted: Sep 11, 2012 2:09 AM
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On 09/10/2012 10:19 PM, Matt J wrote:
> someone <newsboost@gmail.com> wrote in message
> <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 ???

> ================
>
> 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 A-matrix - this is where I have high velocities)...

Anyway - if someone knows anything, can cast light on this, please post
your comments !







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