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Thread Subject:
Solving a Overdeterminated System - More Equantions than unknows

Subject: Solving a Overdeterminated System - More Equantions than unknows

From: Carlos Junior

Date: 15 Apr, 2011 22:55:05

Message: 1 of 4

Hi,

I would like, please, a help to solve a system with 12 equations and 9 unknows. Is there some way ?

The system of equations :

[296 199 1]' = H * [0.1 0.1 1]'
[367 210 1]' = H * [0.2 0.1 1]'
[273 267 1]' = H * [0.1 0.2 1]'
[346 281 1]' = H * [0.2 0.2 1]'

The unknows are the nine elements from H matrix .

Observation:
    To solve H only for one group, I could use "pinv" command , but , what about the 4 groups shown above together ?!
     Example to solve H for only one group (3 equations, 9 unknows )!
[296 199 1]' = H * [0.1 0.1 1]'
H = [296 199 1]' * pinv ( [0.1 0.1 1]' )
H = 29.0196 29.0196 290.1961
        19.5098 19.5098 195.0980
          0.0980 0.0980 0.9804

Very Thanks ,

Carlos
carlosjunior@gmail.com

Subject: Solving a Overdeterminated System - More Equantions than unknows

From: Nasser M. Abbasi

Date: 16 Apr, 2011 02:24:40

Message: 2 of 4

On 4/15/2011 3:55 PM, Carlos Junior wrote:
> Hi,
>
> I would like, please, a help to solve a system with 12 equations and 9 unknows. Is there some way ?

Why not simply A\b ? This will give you least squares solution.

--Nasser

Subject: Solving a Overdeterminated System - More Equantions than unknows

From: Carlos Junior

Date: 16 Apr, 2011 14:35:05

Message: 3 of 4

Hi Nasser,
Thanks by the attention, but I did not understand your solution... I tried now to apply that at MatLab and it did not work !

My necessity is to solve the system below (to find H) :

IMPORTANT : H is a 3x3 matrix. Thus, I have nine unknows.

H = [ h11 h12 h13 ; h21 h22 h23 ; h31 h32 h33 ]

[296 199 1]' = H * [0.1 0.1 1]'
[367 210 1]' = H * [0.2 0.1 1]'
[273 267 1]' = H * [0.1 0.2 1]'
[346 281 1]' = H * [0.2 0.2 1]'

How should I use your proposition A\b ?

Thanks,

Carlos
carlosjunior@gmail.com


"Nasser M. Abbasi" <nma@12000.org> wrote in message <ioaulj$fek$1@speranza.aioe.org>...
> On 4/15/2011 3:55 PM, Carlos Junior wrote:
> > Hi,
> >
> > I would like, please, a help to solve a system with 12 equations and 9 unknows. Is there some way ?
>
> Why not simply A\b ? This will give you least squares solution.
>
> --Nasser

Subject: Solving a Overdeterminated System - More Equantions than unknows

From: Roger Stafford

Date: 16 Apr, 2011 17:51:05

Message: 4 of 4

"Carlos Junior" <carlosjunior@gmail.com> wrote in message <ioc9ep$d1f$1@fred.mathworks.com>...
> Hi Nasser,
> Thanks by the attention, but I did not understand your solution... I tried now to apply that at MatLab and it did not work !
>
> My necessity is to solve the system below (to find H) :
>
> IMPORTANT : H is a 3x3 matrix. Thus, I have nine unknows.
>
> H = [ h11 h12 h13 ; h21 h22 h23 ; h31 h32 h33 ]
>
> [296 199 1]' = H * [0.1 0.1 1]'
> [367 210 1]' = H * [0.2 0.1 1]'
> [273 267 1]' = H * [0.1 0.2 1]'
> [346 281 1]' = H * [0.2 0.2 1]'
>
> How should I use your proposition A\b ?
>
> Thanks,
>
> Carlos
> carlosjunior@gmail.com
- - - - - - - - -
  I think what Nasser has indicated to you is that you are trying to "solve" the matrix equation

 H*A = b

where H is a 3 x 3 matrix of unknowns with

 A = [0.1 0.2 0.1 0.2;
      0.1 0.1 0.2 0.2;
        1 1 1 1];

and

 b = [296 367 273 346;
      199 210 267 281;
        1 1 1 1];

  As you have stated this involves 12 equations but only 9 unknowns so it cannot actually be solved. However matlab's 'slash' operator is designed to give the least squares approximation to it:

 H = b/A

  Notice that it is analogous to doing a right multiply by the inverse of A, though A's size is 3 x 4 and cannot have an actual inverse. Similar statements can be made about the 'backslash' operator.

  Notice also that each of the three rows of H represent an independent set of 4 equations and 3 unknowns. You could have applied least squares analysis to each set separately.

Roger Stafford

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