A family of iterative methods that uses divided differences of first and second orders

作者：Ezquerro J A^*; Grau Sanchez M; Hernandez Veron M A; Noguera M

来源：Numerical Algorithms, 2015, 70(3): 571-589.

DOI：10.1007/s11075-015-9962-0

• Nonlinear equations
• Iterative methods
• Divided difference
• Order of convergence
• Efficiency

The family of fourth-order Steffensen-type methods proposed by Zheng et al. (Appl. Math. Comput. 217, 9592-9597 (2011)) is extended to solve systems of nonlinear equations. This extension uses multidimensional divided differences of first and second orders. For a certain computational efficiency index, two optimal methods are identified in the family. Semilocal convergence is shown for one of these optimal methods under mild conditions. Moreover, a numerical example is given to illustrate the theoretical results.

• 出版日期2015-11