New third order nonlinear solvers for multiple roots
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Two third order methods for finding multiple zeros of nonlinear functions are developed. One method is based on Chebyshev’s third order scheme (for simple roots) and the other is a family based on a variant of Chebyshev’s which does not require the second derivative. Two other more efficient methods of lower order are also given. These last two methods are variants of Chebyshev’s and Osada’s schemes. The informational efficiency of the methods is discussed. All these methods require the knowledge of the multiplicity. Published by Elsevier Inc.
The article of record as published may be found at http://dx.doi.org/10.1016/j.amc.2008.01.031
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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