Fitting 8 equations simultaneously with three parameters

I have 8 equations each with three parameters (A, B, and C) to be fitted. For example,

Eq. 1: 2A+3B+5C-1=0

Eq. 2: -5A+2B-10C+12=0 and so on

I would like to fit the three parameters so that all the 8 equations almost hold simultaneously. Having looked at other posts, it seems that lsqnonlin may be the right choice. I am not looking for the actual solution but I would appreciate a yes or no to the use of lsqnonlin for this problem.

Thanks,

Vahid

Answer 1

[Torsten]

If all 8 equations are linear in the fitting parameters like in your example from above, "lsqlin" instead of "lsqnonlin" would be the code to use. If this is not the case, yes: use "lsqnonlin".

[Vahid Askarpour]

Thanks Torsten for the tip. They are all linear and I will be using lsqlin.

[Torsten]

If there are no constraints on the solution parameters, @Star Strider 's suggestion is also possible to use:

% Eq. 1: 2A+3B+5C-1=0
% Eq. 2: -5A+2B-10C+12=0
% Eq. 3: 9A-B+2C+5=0  
% Eq. 4: 4A-7B+6C-13=0

ABC = lsqlin([2 3 5; -5 2 -10; 9 -1 2; 4 -7 6],[1; -12; -5; 13])

ABC = 3×1

-1.0118 -1.2492 1.4242

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ABC = [2 3 5; -5 2 -10; 9 -1 2; 4 -7 6] \ [1; -12; -5; 13]

ABC = 3×1

-1.0118 -1.2492 1.4242

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Answer 2

[Star Strider]

You might be able to use the mldivide, \ function --

Example --

% Eq. 1: 2A+3B+5C-1=0
% Eq. 2: -5A+2B-10C+12=0
% Eq. 3: 9A-B+2C+5=0                          % <- ADDED

ABC = [2 3 5; -5 2 -10; 9 -1 2] \ [1; -12; -5]

ABC = 3×1

-1.0284 -1.3785 1.4385

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fprintf('\nA = %9.5f\nB = %9.5f\nC = %9.5f\n',ABC)

A =  -1.02839
B =  -1.37855
C =   1.43849

.

[Vahid Askarpour]

Thank you Star Strider and Torsten for your comments. I used both your suggestions and I get exactly the same answer.

Cheers,

Vahid