Let's consider again the equation (1): (1)
where
Let's expanse the function
(5)
that is equivalent to exchanging of function
Then from (1) and (5) follows: (6) If to accept for zero approach, the formula (6) can be used for a finding of the following, the 1-st approach: (7)
From here it follows, that the (
(8)
The correlation (8) also is a
The
1) zero approach is chosen close enough to a root of the equation
2) derivative
3) derivative
The last condition means, that no two roots existed the close one from another, and joint performance of conditions 2) and 3) is similar to the requirement in a method of iterations . The process (8) is considered completed, if – the given accuracy of the solution. Newton-Raphson method finds a wide application for the solution of the high order systems of nonlinear equations. You can see examples here and here . |

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