AM  Vol.7 No.11 , July 2016
A Remarkable Chord Iterative Method for Roots of Uncertain Multiplicity
Abstract: In this note we at first briefly review iterative methods for effectively approaching a root of an unknown multiplicity. We describe a first order, then a second order estimate for the multiplicity index m of the approached root. Next we present a second order, two-step method for iteratively nearing a root of an unknown multiplicity. Subsequently, we introduce a novel chord, or a two- step method, not requiring beforehand knowledge of the multiplicity index m of the sought root, nor requiring higher order derivatives of the equilibrium function, which is quadratically convergent for any , and then reverts to superlinear.
Cite this paper: Fried, I. (2016) A Remarkable Chord Iterative Method for Roots of Uncertain Multiplicity. Applied Mathematics, 7, 1207-1214. doi: 10.4236/am.2016.711106.

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