A new approach for the bigeometric newton method

Yıl 2023, Cilt: 11 Sayı: 2, 235 - 240, 25.12.2023

Numan Yalçın Ercan Celık

https://doi.org/10.51354/mjen.1372839

Öz

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).

Anahtar Kelimeler

Bigeometric analysis, Bigeometric Newton method, Quadratic convergence, Bigeometric Taylor expansion

Kaynakça

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