### One Point Iteration

 The simple one point iteration method which is introduced for solving non-linear equations now can be extended for solution of the system of non-linear equations. Suppose an arbitrary system of non-linear equations which can be define as follows:   f1 ( x1 , x2 ,… xn ) = 0 f2 ( x1 , x2 ,… xn ) = 0 . . . fn ( x1 , x2 ,… xn ) = 0.   This system of non-linear equation can easily be rewritten as follows:   x1 = g1 ( x1 , x2 ,… xn ) x2 = g 2 ( x1 , x2 ,… xn ) . . . xn = g n ( x1 , x2 ,… xn ) .   Choosing a starting point, the new guess of roots can be found from above equations. Unfortunately, the convergence condition of one point iteration method is very restrictive as follows:   The algorithm of one point iteration method is for solving system of non-linear equations similar to the simple one point iteration method algorithm. This algorithm can be written as follows:   Step 1: Choose X0 = [x1,x2,…,xn] as a starting point. Step 2: Let  X = G(X0) where G=[g1,g2,…,gn]. Step 3: If ||x-x0||