I have a nonlinear system of algebraic equations of special kind:$$   \begin{array}{rcl}     x_{i}+y_{i}+z_{0,1}+c_{i,1}z_{1,1} & = & d_{i,1}, \\   x_{i}^2 + y_{i}^2 + z_{0,2} + c_{i,1} z_{1,2} + c_{i,2} z_{2,2} & = & d_{i,2} \\   \ldots & = & \ldots \\   x_{i}^{m} + y_{i}^{m} +z_{0,m}+c_{i,1} z_{1,m} + \ldots + c_{i,m} z_{m,m} & = & d_{i,m}   \end{array}$$where $i = 1,\ldots.k$ and number of equations is not less than number of unknowns.  I have to find $(x_{i},y_{i},z_{i,j})$; $c_{i,j}$ and $d_{i,j}$ are known. Is there some numerical method that take in account specificity of this system? If not, please tell me which numerical method will work better with this system?
Numerical method for nonlinear system of algebraic equations of special type
linear algebra;numerics;nonlinear equations