Potra-Pták iterative method with memory (Q2449034)

Summary: The problem is to extend the method proposed by \textit{F. Soleymani} et al. [Math. Comput. Modelling 56, No. 5--6, 97--104 (2012; Zbl 1255.65096)] to a method with memory. Following this aim, a free parameter is calculated using Newton's interpolatory polynomial of the third degree. So the \(R\)-order of convergence is increased from 4 to 6 without any new function evaluations. Numerically the extended method is examined along with comparison to some existing methods with the similar properties.