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New third order nonlinear solvers for multiple roots. (English) Zbl 1151.65041
Summary: 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 {\it N. Osada}’s schemes [J. Comput. Appl. Math. 51, No. 1, 131--133 (1994; Zbl 0814.65045)]. The informational efficiency of the methods is discussed. All these methods require the knowledge of the multiplicity.

65H05Single nonlinear equations (numerical methods)
Full Text: DOI
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