On a New Generalised Iteration Method in the PSO-Based Newton-Like Method

The root-finding problem is very important in many applications and has become an extensive research field. One of the directions in this field is the use of various iteration schemes. In this paper, we propose a new generalised iteration scheme. The schemes like Mann, Ishikawa, Das-Debata schemes are special cases of the proposed iteration. Moreover, we use the proposed iteration with the PSO-based Newton-like method in two tasks. In the first task, we search for the roots, whereas in the second one for patterns with aesthetic features. The obtained results show that the proposed iteration can decrease the average number of iterations needed to find the roots and that we can generate patterns with potential artistic applications.