Solve a set of implicit equations

Hi, I am trying to find a solution for a set of implicit equations in the form: b_i=f(x_1,x_2,...,x_i,...,x_n) where b are known and x are the unknowns which can't be algebraically isolated (the exact equations are attached in the image). In the problem I am trying to solve now n=50-100. So far, I was only able to find solvers that deal with differential equations and sets of linear equations. Can anyone please advise on how to approach this? Thanks.

Answer 1

[Torsten]

help fsolve

Best wishes

Torsten.

[Ronen]

Thanks,

I don't have the optimization toolbox that contains this function, so I can't immediately try it. Any idea if it could converge for a system of 70 equations?

Best.

[Torsten]

As a first test on the difficulty of your system of equations, you could also try fminsearch on the objective function

sum_{i=1}^{N} (b_i-f(x_1,x_2,...,x_i,...,x_n))^2

Or try Scilab:

https://help.scilab.org/doc/5.5.2/en_US/fsolve.html

Best wishes

Torsten.