TITLE:
A Remarkable Chord Iterative Method for Roots of Uncertain Multiplicity
AUTHORS:
I. Fried
KEYWORDS:
Iterative Methods, Unknown Root Multiplicity, Two-Step Methods
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.11,
July
11,
2016
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.