New third-order Newton-like method with lower iteration number and lower TNFE

Pantelimon George Popescu, Radu Constantin Poenaru, Florin Pop

Abstract: This paper presents a new iterative Newton-like method for solving nonlinear equations which is firstly compared with very recent results and we show that it reaches the solution in a lower number of iterations and with a lower total number of function evaluations, considering a variable length of the floating point arithmetic with multi-precision. Then, considering a fix length of the floating point arithmetic with multi-precision, we have compared it with other methods and we have obtained similar results.