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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Corina Karim
Brawijaya University
Mathematics

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Comparing Newton Raphson and Stochastic Gradient Descent Methods for Traffic Accident in Malang Aldi Rahmad Nur Fauzi; Sobri Abusini; Corina Karim
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.33177

Abstract

This study discusses a comparison between two optimization methods, Newton–Raphson and Stochastic Gradient Descent (SGD), in binary logistic regression modeling to analyze the severity of traffic accidents in Malang Regency. Parameter estimation was carried out using both methods to assess their effectiveness in achieving convergence and producing a well-fitted model. The results show that the Newton–Raphson method failed to achieve convergence despite its fast iteration speed, while the SGD method successfully converged, although it required a large number of iterations. Model evaluation was conducted by examining model fit through log-likelihood values and the Akaike Information Criterion (AIC). The results indicate that the SGD method produced a better-fitting model compared to Newton–Raphson. Additionally, the regression models from each method identified different predictor variables as significant, suggesting that the choice of optimization approach can influence analytical outcomes. These findings highlight the importance of selecting an appropriate optimization method in logistic regression analysis, particularly for complex and imbalanced accident data.
A Multiplicative Extension of Weighted Hadamard Fractional Integrals Almeer Naufal Hakim; Marjono Marjono; Corina Karim
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.43122

Abstract

This paper presents an innovative category of weighted Hadamard fractional integral operators situated within the paradigm of multiplicative calculus. The operator introduced herein broadens the traditional weighted Hadamard fractional integral by integrating the multiplicative framework of non-Newtonian calculus, thereby establishing a cohesive linkage between weighted fractional analysis and multiplicative fractional calculus. We delineate the formulation of both the left- and right-sided multiplicative weighted Hadamard fractional integral operators and explore their core analytical characteristics. Specifically, a multiplicative linearity property is demonstrated, the continuity of the logarithmic representation of the operator is affirmed, and boundedness results are extracted in weighted Lebesgue-type spaces through the application of Hölder's inequality. Furthermore, we establish that the proposed operators comply with a semigroup property, which ensures alignment with the classical framework of fractional integration. These findings illustrate that the introduced operators maintain crucial structural attributes of weighted fractional integrals while seamlessly extending them to the multiplicative context. The theoretical framework developed herein lays a foundational basis for subsequent explorations in multiplicative fractional calculus, fractional integral inequalities, and associated applications within the realm of mathematical analysis.
Co-Authors Aldi Rahmad Nur Fauzi Almeer Naufal Hakim Marjono, Marjono Sobri Abusini