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 meth...
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| Format: | Article |
| Language: | English |
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Kyrgyz Turkish Manas University
2023-12-01
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| Series: | MANAS: Journal of Engineering |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3461135 |
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| _version_ | 1832543376138829824 |
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| author | Numan Yalçın Ercan Celık |
| author_facet | Numan Yalçın Ercan Celık |
| author_sort | Numan Yalçın |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-9136be2fad194af6a045ae0e7edf209d |
| institution | Kabale University |
| issn | 1694-7398 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Kyrgyz Turkish Manas University |
| record_format | Article |
| series | MANAS: Journal of Engineering |
| spelling | doaj-art-9136be2fad194af6a045ae0e7edf209d2025-02-03T11:47:05ZengKyrgyz Turkish Manas UniversityMANAS: Journal of Engineering1694-73982023-12-0111223524010.51354/mjen.13728391437A new approach for the bigeometric newton methodNuman Yalçın0https://orcid.org/0000-0002-8896-6437Ercan Celık1https://orcid.org/0000-0002-1402-1457GUMUSHANE UNIVERSITYKyrgyz-Turkish Manas UniversityIn 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).https://dergipark.org.tr/en/download/article-file/3461135bigeometric analysisbigeometric newton methodquadratic convergencebigeometric taylor expansion |
| spellingShingle | Numan Yalçın Ercan Celık A new approach for the bigeometric newton method MANAS: Journal of Engineering bigeometric analysis bigeometric newton method quadratic convergence bigeometric taylor expansion |
| title | A new approach for the bigeometric newton method |
| title_full | A new approach for the bigeometric newton method |
| title_fullStr | A new approach for the bigeometric newton method |
| title_full_unstemmed | A new approach for the bigeometric newton method |
| title_short | A new approach for the bigeometric newton method |
| title_sort | new approach for the bigeometric newton method |
| topic | bigeometric analysis bigeometric newton method quadratic convergence bigeometric taylor expansion |
| url | https://dergipark.org.tr/en/download/article-file/3461135 |
| work_keys_str_mv | AT numanyalcın anewapproachforthebigeometricnewtonmethod AT ercancelık anewapproachforthebigeometricnewtonmethod AT numanyalcın newapproachforthebigeometricnewtonmethod AT ercancelık newapproachforthebigeometricnewtonmethod |