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

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nasrin
nasrin 2012-7-25
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
Jan 2012-7-25
Dear nasrin, of course we cannot access the files on your harddisk. Imagine what this would mean!

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Sargondjani
Sargondjani 2012-7-25
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
Sargondjani 2012-7-31
fminsearchcon does exist in the 'file exchange', ie. you have to download it.
MJTHDSN
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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