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:
This system of non-linear equation can easily be rewritten as follows:
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:
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G=[g_{1},g_{2},…,g_{n}].
<e then let root = X, else X ; go to step 2._{0} = X
e: Acceptable approximated error. (Source Code in C++) |