Thread Subject: Matlab: least square fit with more than one variables

Hello,
Is there anyone can help me with the following problem in Matlab?
Suppose I have a function:

sqrt((1/N)*sum((x+(a+b*x+c*x*x)*(y-800)-z)^2)),

where N is number of data points, x,y,z are known experiment data (1D arrays with same size) which can be read from file. Will need to find a,b,c so the above function is minimized.
Any help is highly appreciated.
Thanks

On Jun 7, 9:39=A0am, itubeusa <itube...@yahoo.com> wrote:
> Hello,
> Is there anyone can help me with the following problem in Matlab?
> Suppose I have a function:
>
> sqrt((1/N)*sum((x+(a+b*x+c*x*x)*(y-800)-z)^2)),
>
> where N is number of data points, x,y,z are known experiment data (1D arra=
ys with same size) which can be read from file. Will need to find a,b,c so t=
he above function is minimized.
> Any help is highly appreciated.
> Thanks

Your notation is confusing. It looks like it can be reduced to

Minimize w'*w

where

w =3D x - z + ( y - 800 ) .* ( a + b * x + c * x.^2)

Hope this helps.

Greg

On Sat, 7 Jun 2008 07:11:45 -0700 (PDT), Greg Heath
<heath@alumni.brown.edu> wrote:

>On Jun 7, 9:39 am, itubeusa <itube...@yahoo.com> wrote:
>> Hello,
>> Is there anyone can help me with the following problem in Matlab?
>> Suppose I have a function:
>>
>> sqrt((1/N)*sum((x+(a+b*x+c*x*x)*(y-800)-z)^2)),
>>
>> where N is number of data points, x,y,z are known experiment data (1D arrays with same size) which can be read from file. Will need to find a,b,c so the above function is minimized.
>> Any help is highly appreciated.
>> Thanks
>
>Your notation is confusing. It looks like it can be reduced to
>
>Minimize w'*w
>
>where
>
>w = x - z + ( y - 800 ) .* ( a + b * x + c * x.^2)
>
>Hope this helps.
>
>Greg

If you follow-up on Greg's suggestion, this becomes a simple least
squares problem that can be solved with the backslash operator. Think
of the equation as

(x-z) = a*(y-800) + b*(y-800)*x + b*(y-800)*x.^2

-Dick Startz