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2018 On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals
Jukkrit Daengsaen, Anchalee Khemphet
Abstr. Appl. Anal. 2018: 1-6 (2018). DOI: 10.1155/2018/7345401

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.

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Jukkrit Daengsaen. Anchalee Khemphet. "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

Information

Received: 2 March 2018; Revised: 24 May 2018; Accepted: 29 May 2018; Published: 2018
First available in Project Euclid: 19 September 2018

zbMATH: 06929593
MathSciNet: MR3827819
Digital Object Identifier: 10.1155/2018/7345401

Rights: Copyright © 2018 Hindawi

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