چکیده (انگلیسی):

In recent papers (Appl.Math.Comput.140 (2003) 419–426; Appl.Math.Lett.13 (2000) 87–93) a new modifcation of the Newton’s method (mNm) which produces iterative methods with order of convergence three have been proposed.Here we study the order of convergence of such methods when we have multiple roots.We prove that the order of convergence of the mNm go down to one but, when the multiplicity p is known, it may be rised up to two by using two di8erent types of correction.When p is unknown we show that the two most e9cient methods in the family of the mNm converge faster than the classical Newton’s method.