A new approach for the bigeometric newton method

In this study, quadratic convergent new bigeometric Newton's method (nBGNM) was developed. For this, the basic definitions and theorems of bigeometric analysis, which is one of the non-Newtonian analysis, were used. Using the bigeometric Taylor expansion, a convergence analysis of this new method was given. Also, the new bigeometric Newton method (nBGNM) was compared in detail with the geometric (multiplicative) Newton method (GNM) and the classical Newton method (NM).

Keyword: bigeometric analysis; bigeometric newton method; quadratic convergence; bigeometric taylor expansion

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Publication Name
(dc.title)		A new approach for the bigeometric newton method
Author/s
(dc.contributor.yazarlar)		Numan YALÇIN, Ercan CELIK
Publication type
(dc.type)		Makale
Publication year
(dc.date.issued)		2023
National/International
(dc.identifier.ulusaluluslararasi)		Ulusal
Source
(dc.relation.journal)		MANAS Journal of Engineering (MJEN)
Number
(dc.identifier.issue)		2
Volume/Issue
(dc.identifier.volume)		11
Page
(dc.identifier.startpage)		325-240
ISSN/ISBN
(dc.identifier.issn)		Online ISSN: 1694-7398
Publisher
(dc.publisher)		Kyrgyz - Turkish Manas University
Databases
(dc.contributor.veritaban)		Ulakbim (DergiPark)
Databases
(dc.contributor.veritaban)		EBSCOHost
Index Type
(dc.identifier.index)		Alan Indeks
Abstract
(dc.description.abstract)		In this study, quadratic convergent new bigeometric Newton's method (nBGNM) was developed. For this, the basic definitions and theorems of bigeometric analysis, which is one of the non-Newtonian analysis, were used. Using the bigeometric Taylor expansion, a convergence analysis of this new method was given. Also, the new bigeometric Newton method (nBGNM) was compared in detail with the geometric (multiplicative) Newton method (GNM) and the classical Newton method (NM).
Abstract
(dc.description.abstract)		Keyword: bigeometric analysis; bigeometric newton method; quadratic convergence; bigeometric taylor expansion
URL
(dc.rights)		https://dergipark.org.tr/tr/pub/mjen/issue/81663/1372839
DOI
(dc.identifier.doi)		10.51354/mjen.1372839
Faculty / Institute
(dc.identifier.fakulte)		Mühendislik Fakültesi
Department
(dc.identifier.bolum)		Uygulamalı Matematik ve Enformatik Bölümü
Author(s) in the Institution
(dc.contributor.author)		Ercan ÇELİK
Kayıt No
(dc.identifier.kayitno)		BL2D0DE5DA
Record Add Date
(dc.date.available)		2023-12-29
Notes (Publication year)
(dc.identifier.notyayinyili)		2023
Subject Headings
(dc.subject)		bigeometric analysis
Subject Headings
(dc.subject)		bigeometric newton method
Subject Headings
(dc.subject)		quadratic convergence
Subject Headings
(dc.subject)		bigeometric taylor expansion
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