Extension of Murakami's high-order non-linear solver to multiple roots

Authors:
B. Neta
Affiliations:
Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, USA
Venue:
International Journal of Computer Mathematics
Year:
2010

Citing 0
Cited 5

New families of nonlinear third-order solvers for finding multiple roots

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Constructing higher-order methods for obtaining the multiple roots of nonlinear equations

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Fifth-order iterative method for finding multiple roots of nonlinear equations

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Iterative methods for solving nonlinear equations with finitely many roots in an interval

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On the convergence radius of the modified Newton method for multiple roots under the center---Hölder condition

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Abstract

Several one-parameter families of fourth-order methods for finding multiple zeros of non-linear functions are developed. The methods are based on Murakami's fifth-order method (for simple roots) and they require one evaluation of the function and three evaluations of the derivative. The informational efficiency of the methods is the same as the previously developed methods of lower order. For a double root, the method is more efficient than all previously known schemes. All these methods require the knowledge of multiplicity.