MULTIPLE ROOTS

This method solve the problem that a derivative can be equal to zero in the Newton method, as this decreases the speed of convergence leads to a division by zero.

In the case that a root xv can be repeated multiple times on a function, which means it follows the expression , where m is the multiplicity  and q ( x ) ≠ 0 , methods such as Newton and secant tend to fail. To solve these problems the following expression is proposed to calculate xn + 1 in the iterative system.

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The convergence of this methos is cuadratic.