TY - JOUR
T1 - Eighth-order methods with high efficiency index for solving nonlinear equations
AU - Liu, Liping
AU - Wang, Xia
PY - 2010/1/1
Y1 - 2010/1/1
N2 - In this paper, we derive a new family of eighth-order methods for solving simple roots of nonlinear equations by using weight function methods. Per iteration these methods require three evaluations of the function and one evaluation of its first derivative, which implies that the efficiency indexes are 1.682. Numerical comparisons are made to show the performance of the derived methods, as shown in the illustration examples. © 2009 Elsevier Inc. All rights reserved.
AB - In this paper, we derive a new family of eighth-order methods for solving simple roots of nonlinear equations by using weight function methods. Per iteration these methods require three evaluations of the function and one evaluation of its first derivative, which implies that the efficiency indexes are 1.682. Numerical comparisons are made to show the performance of the derived methods, as shown in the illustration examples. © 2009 Elsevier Inc. All rights reserved.
KW - Convergence order
KW - Efficiency index
KW - Eighth-order convergence
KW - Nonlinear equations
KW - Weight function methods
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U2 - 10.1016/j.amc.2009.10.040
DO - 10.1016/j.amc.2009.10.040
M3 - Article
SN - 0096-3003
VL - 215
SP - 3449
EP - 3454
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 9
ER -