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||<e then let root = X, else X0 = X ; go to step 2. Step 4: End.
e: Acceptable approximated error.
(Source Code in C++)
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