On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals

Abstract EN

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.