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    A Remarkable Chord Iterative Method for Roots of Uncertain Multiplicity

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    Date
    2016-07
    Author
    Fried, I.
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    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.
    URI
    http://dx.doi.org/10.4236/am.2016.711106
    http://hdl.handle.net/123456789/876
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    • Physics & Mathematics [63]

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