Interval Ostrowski-type methods with guaranteed convergence

Bakhtiari, Parisa; Lotfi, Taher; Mahdiani, Katayoun; Soleymani, Fazlollah

doi:10.1007/s11565-012-0174-4

Cited by 9 publications

(19 citation statements)

References 15 publications

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“…As a basis for our research we use the methods discussed in the article [14]. We look for a root of a real function f (x).…”

Section: Interval Newton's Methodsmentioning

confidence: 99%

“…So, convergence of the sequence follows [13,20,21]. It should be noted that some special cases of (1) have been discussed in [14] in more details.…”

Section: Theorem 2 ([13]mentioning

confidence: 99%

“…Interval analysis is formally presented by Moore [13]. In article [14], the authors have described iterative formulas proposed by Ostrowski [15] and based on Newton's interval method and offer interval modifications of these iterative patterns.…”

Section: Introductionmentioning

confidence: 99%

“…We modify Kou's method in interval form to see are they fast and stable in this interval form. We use the methodology for the research, analysis and comparison of iterative schemes applied by authors in articles [14,16] and others. For each of proposed methods, a theorem of convergence and a proof of the theorem is shown.…”

Section: Introductionmentioning

confidence: 99%

“…The second aim is to compare the new interval schemes to Newton's well-known interval scheme and the schemes described in the article [18]. We look at features reviewed in articles [14] and [19] to assess the effectiveness of the offered modifications.…”

Section: Introductionmentioning

confidence: 99%

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Interval Methods with Fifth Order of Convergence for Solving Nonlinear Scalar Equations

Ivanov

Mateva

2019

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In this paper, based on Kou’s classical iterative methods with fifth-order of convergence, we propose new interval iterative methods for computing a real root of the nonlinear scalar equations. Some numerical experiments have executed with the program INTLAB in order to confirm the theoretical results. The computational results have described and compared with Newton’s interval method, Ostrowski’s interval method and Ostrowski’s modified interval method. We conclude that the proposed interval schemes are effective and they are comparable to the classical interval methods.

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“…As a basis for our research we use the methods discussed in the article [14]. We look for a root of a real function f (x).…”

Section: Interval Newton's Methodsmentioning

confidence: 99%

“…So, convergence of the sequence follows [13,20,21]. It should be noted that some special cases of (1) have been discussed in [14] in more details.…”

Section: Theorem 2 ([13]mentioning

confidence: 99%