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

Jukkrit Daengsaen and Anchalee Khemphet

Abstract and Applied Analysis, 2018, vol. 2018, issue 1

Abstract: 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.

Date: 2018
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https://doi.org/10.1155/2018/7345401

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2018:y:2018:i:1:n:7345401

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