In solution of non-linear algebraic equations, now researchers suggest Holomorphic Embedding solutions. These are supposed to give a non-iterative unique solution. And reliable at the same time.
Homotopy methods using a real number for embedding (say Lamda) are also suggested. It would be interesting to me to see a simple tutorial on the issue. Let us take say, three non-linear equations in x1, x2 and x3. and solve by both the methods so we can know how each one id different from the other. Thanks to research gate..