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

Authors:
Xiaojian Zhou;Xin Chen;Yongzhong Song
Affiliations:
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, PR China and School of Science, Nantong University, Nantong 226007, PR China;Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, PR China;Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 4
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Abstract

This paper concentrates on iterative methods for obtaining the multiple roots of nonlinear equations. Using the computer algebra system Mathematica, we construct an iterative scheme and discuss the conditions to obtain fourth-order methods from it. All the presented fourth-order methods require one-function and two-derivative evaluation per iteration, and are optimal higher-order iterative methods for obtaining multiple roots. We present some special methods from the iterative scheme, including some known already. Numerical examples are also given to show their performance.