I am trying to perform model reduction on a system of algebraic equations by reducing the number of variables in the system. In doing so I am not trying to remove equations from the system, rather I am trying to remove variables from the system and replace it with an already existing variable. For example:
a + b + c = 3
a + b + d = 4
a + b + e = 5
and replace this with:
a + b + c = 3
a + b + d = 4
a + b + d = 5
There will not be an exact solution but I want to minimize error. I am working with a much larger set of functions than was given above. What suggested routes could I utilize to minimize the error that occurred in this problem?
I was looking into SPSA where I would model the mean of the sum of solutions - what my estimated guess would give as the mean of the sum of solutions as the objective function and iterately change the parameters such that error is minimized for that however I am not confident this will work or is even a good way to solve this problem.
I should also mention that I will need to normalize the errors. By that, I am needing to accept larger errors such that I can reduce the sigma of the error seen across each of the individual equations. Reducing the sigma is critical.
My goal is to determine how many variables I can remove while maintaining an acceptable error rate with an acceptable sigma seen across all the errors.