TY  - JOUR
ID  - Soleymani2013
LB  - Soleymani2013
AU  - Soleymani, Fazlollah
TI  - Some efficient seventh-order derivative-free families in root-finding
ST  - Some efficient seventh-order derivative-free families in root-finding
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2013
VL  - 33
IS  - 1
SP  - 163
EP  - 173
DO  - http://dx.doi.org/10.7494/OpMath.2013.33.1.163
UR  - http://dx.doi.org/10.7494/OpMath.2013.33.1.163
AB  - The interest in efficient root-finding iterations is nowadays growing and influenced by the widespread use of high-speed computers. On the other hand, the calculation of derivatives is often hard, when the problems are formulated in terms of nonlinear equations and as a result, the importance of derivative-free methods emerges. For these reasons, some efficient three-step families of iterations for solving nonlinear equations are suggested, where the analytical proofs show their seventh-order error equations consuming only four function evaluations per iteration. We employ hard numerical test problems to illustrate the accuracy of the new methods from the families.
KW  - numerical analysis
KW  - derivative-free families
KW  - order
KW  - iterative methods
SN  - 1232-9274
ER  -