how to solve a system of equations with n equation and m unknown (m>n)?

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nasrin 2012-7-25

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评论： MJTHDSN 2018-4-12

to solve this equation "f = a+b θs + c θv cos(φ)" : unknowns are : f, a, b & c i am working on space image and can calculate θs, θv & φ for all pixel of image so i can write a lot of equation. and there are 2 constraint :

http://postimage.org/image/4a0qy3973/

How do I solve this system of equations?

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Jan 2012-7-25

Dear nasrin, of course we cannot access the files on your harddisk. Imagine what this would mean!

nasrin 2012-7-25

编辑：nasrin 2012-7-25

sorry, it was wrong. link : http://postimage.org/image/4a0qy3973/

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Answer 1

Sargondjani 2012-7-25

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i think fmincon (constrained optimization) will work best... if you try to minimize some error use as the objective: objective=error^2.

if you dont have the optimization toolbox you can try fminsearchcon from the file exchange (but this only works properly for a couple of variables at most)

note that fmincon can only find one local solution and it requires a continuous function + continuous derivate. if not continuous, then you should try genetic algorithm

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Sargondjani 2012-7-31

fminsearchcon does exist in the 'file exchange', ie. you have to download it.

MJTHDSN 2018-4-12

Dear Matlabers,

I have a similar question but a little bit confusing. Let`s assume we have 6 equations as below:

EQ1:a{{(L^2)*(Z^2)+(L^2)*(M^2)-2*L*(Z^2)+(Z^2)}}=(L^2)*(T^2)-2*L*(T^2)+ (T^2)-(2*L*T*B)+(T*B)+(B^2)

EQ2: b{{(L^2)*(Z^2)+(L^2)*(M^2)-2*L*(Z^2)+(Z^2)}}=(L^2)*(T^2)+(2*L*T*B)+(B^2)

EQ3: c{{(L^2)*(Z^2)+(L^2)*(M^2)-2*L*(Z^2)+(Z^2)}}=(T^2)+(2*T*B)+(B^2)

EQ4:d{{(L^2)*(Z^2)+(L^2)*(M^2)-2*L*(Z^2)+(Z^2)}}=(L^2)*(T^2)-2*L*(T^2)+ (T^2)-(2*L*T*B)-(T*B)+(B^2)

EQ5: e{{(L^2)*(Z^2)+(L^2)*(M^2)-2*L*(Z^2)+(Z^2)}}=(L^2)*(T^2)-(2*L*T*B)+(B^2)

EQ6: f{{(L^2)*(Z^2)+(L^2)*(M^2)-2*L*(Z^2)+(Z^2)}}=(T^2)-(2*T*B)+(B^2)

in the equations above a,b,c,d,e and f are the numerical known values (0.543 for example). So we have 6 equations with 5 unknowns as L, Z, M, T and B.

Can you please give me cues how to solve the equations to find these unknowns using MATLAB.

Best Regards,

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