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

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

© 2018 Jukkrit Daengsaen and Anchalee Khemphet. 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...

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Main Authors: Jukkrit Daengsaen, Anchalee Khemphet
Format: Journal
Published: 2018
Subjects:
Mathematics
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85050179926&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/58829
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-588292018-09-05T04:33:12Z 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 Mathematics © 2018 Jukkrit Daengsaen and Anchalee Khemphet. 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. 2018-09-05T04:33:12Z 2018-09-05T04:33:12Z 2018-01-01 Journal 16870409 10853375 2-s2.0-85050179926 10.1155/2018/7345401 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85050179926&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58829
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
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
description © 2018 Jukkrit Daengsaen and Anchalee Khemphet. 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.
format Journal
author Jukkrit Daengsaen
Anchalee Khemphet
author_facet Jukkrit Daengsaen
Anchalee Khemphet
author_sort Jukkrit Daengsaen
title On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals
title_short On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals
title_full On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals
title_fullStr On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals
title_full_unstemmed On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals
title_sort on the rate of convergence of p-iteration, sp-iteration, and d-iteration methods for continuous nondecreasing functions on closed intervals
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85050179926&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/58829
_version_ 1681425138422120448

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