We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D-iteration converges faster than the others under the same computational cost. Moreover, the analogue of their convergence theorem holds for D-iteration.
"On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals." Abstr. Appl. Anal. 2018 1 - 6, 2018. https://doi.org/10.1155/2018/7345401