Extension of Murakami’s High order nonlinear solver to multiple roots
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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 oflov.1er order. For a double root, the method is more efficient than all previously known schemes. All these methods require the knowledge ofmultiplicity.
International Journal of Computer Mathematics, 8, (2010), 1023-1031, DOI: 10.1080/0020716080227226The article of record as published may be located at http://dx.doi.org/10.1080/0020716080227226
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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