Solve Nonlinear System of Equations

[phil0stine]

Hi, I have a set of vectors that I would like to solve for in a nonlinear system of equations.

I have tried to use scipy.fsolve to solve the system, but without success. I believe the problem is that scipy expects the same number of inputs as outputs. I have a 12x1 input vector, but I can only generate 9 independent equations.

I would appreciate any help with this, for example how I could over-constrain the problem, or am I missing something?

The vectors {C,R₁,R₂,R₃} are all (3x1). There are also a set of (3x1) vectors {S₁,S₂,S₃} that are known.

The equations are as follows:

C^TR₁=S₁ (1)

C^TR₂=S₂ (2)

C^TR₃=S₃ (3)

and finally

[R₁ R₂ R₃]^T[R₁ R₂ R₃]=I

which can be reduced to

R₁^TR₁=R₂^TR₂=R₃^TR₃=1 (4,5,6)

R₁^TR₂=R₂^TR₃=R₃^TR₁=0 (7,8,9)

R₂^TR₁=R₃^TR₂=R₁^TR₃=0 Would give me 12 equations, but they are exactly the same as Equations 7,8,9.

So I don't know how to proceed. I would appreciate if anybody could point me in a direction, or to a matlab/scipy routine.

 

[phil0stine]

I think I have it, I cannot solve the system without an additional set of constraints.