Re: Ask: Multi-dimensional linear fitting or solving an over-determined inhomogeneous linear equation

Hi Victor,

Thanks a lot for your reply.

Maybe I didn't make myself clear in last email, so I cc this email to roottalk.

I think 9 conditions for 5 variables is fine. Taking a 2-D linear fit as example,
I have 9 observed points (x_i, y_i) with error ( delta(x_i), delta(y_i) ), where i from 1 to 9.

And I use a 2-parameter linear equation-- ax+b = y to fit this points and estimate the parameters: a and b.

Here I have 2 unknown and 9 constraints.

In my question, the 2-D example become 5-D, then the number of parameter become 5.
But the core issue is still the same in principle.

The above is just my personal opinion, please let me know your further comments.

Cheers

Lei

On 6/25/2012 17:39, Victor Perev wrote:
> Hi Lei,
> your system can not be solved. You have 9 conditions for 5 variables
> which contradict each other.
> Existence of errors could not help here. Probably there is some
> mistake, in the way where you
> got this system.
> Victor
>
>
> Victor M. Perevoztchikov perev_at_bnl.gov <mailto:perev_at_bnl.gov>
> Brookhaven National Laboratory MS 510A
> PO Box 5000, Upton, NY 11973-5000
> Tel: office 631-344-7894; fax 631-344-4206
>
> ----- Original Message -----
> *From:* Lei Zhang <mailto:lei.zhang_at_cern.ch>
> *To:* roottalk_at_root.cern.ch <mailto:roottalk_at_root.cern.ch>
> *Sent:* Monday, June 25, 2012 4:51 AM
> *Subject:* [ROOT] Ask: Multi-dimensional linear fitting or solving
> an over-determined inhomogeneous linear equation
>
> Dear ROOT experts:
>
> I have solve an over-determined inhomogeneous linear equation in
> which all the observables have error.
> The following is equation I need to solve:
>
> A*X=B,
>
> here A is 9x5 matrix with known elements, X is 5x1 matrix with
> unknown elements, and B is 9x1 matrix with known elements.
> All the element of A and B have errors.
>
> May I ask whether there is a proper way to solve this question?
>
> The best way I can come up with is:
> Assuming the 9x5 matrix A and 9x1 matrix B are 9 points (with
> errors) in 5+1 space, we use a 5 parameter (x_i) linear equation
> to fit it.
> After this, we could get that 5x1 matrix--X (x_i).
>
> But here my question is how can I construct a 5 parameter linear
> equation to do fitting in 5-dimensional space?
>
> Thank you in advance.
>
> Best regards
>
> Lei
>
>
>
>
>
>
Received on Tue Jun 26 2012 - 23:47:52 CEST