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All Journal Jurnal ELTIKOM : Jurnal Teknik Elektro, Teknologi Informasi dan Komputer Journal of Information Systems and Informatics
Syaharuddin
University of Muhammadiyah Mataram
Aerospace Engineering Computer Science & IT Control & Systems Engineering Electrical & Electronics Engineering Engineering

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Accuracy Comparison of Multivariate Newton-Raphson and Newton-Kantorovich Methods through Numerical Simulation in Nonlinear Systems Syaharuddin; Hendi Hidayah; Mahsup Mahsup; Saba Mehmood; Wasim Raza
Jurnal ELTIKOM : Jurnal Teknik Elektro, Teknologi Informasi dan Komputer Vol. 10 No. 1 (2026)
Publisher : P3M Politeknik Negeri Banjarmasin

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31961/eltikom.v10i1.1971

Abstract

Nonlinear systems of equations often appear in various fields of science and generally cannot be solved analytically, so numerical methods are required. However, previous studies have not provided a direct comparison of the accuracy and efficiency of the Multivariate Newton-Raphson method and the Newton-Kantorovich method when applied to the same nonlinear system, creating a gap in understanding their relative performance. This study aims to analyze and compare the performance of two numerical methods, namely the Newton-Raphson method and the Newton-Kantorovich method, in solving nonlinear systems of equations numerically. The evaluation is based on the convergence rate, result accuracy, and iteration efficiency of each method. The nonlinear system used involves trigonometric, exponential, and polynomial functions. Simulations were conducted twice using three equations directly for each method. The error tolerance was set at 0.001, with a maximum of 100 iterations. The simulation results showed that the Multivariate Newton-Raphson method had the best performance, requiring only 7 iterations to achieve convergence with a very small error of 2.711×10^(-7). In contrast, the Newton-Kantorovich method required 21 iterations and produced an error of 6.770×10^(-5), indicating slower convergence and lower efficiency. Based on these results, it can be concluded that the Multivariate Newton-Raphson method is the more accurate and efficient method for solving nonlinear systems of equations through numerical simulation. This finding contributes to the selection of an appropriate numerical method and opens opportunities for further exploration in higher-dimensional systems.
A Hybrid ACO-BPNN-XGBoost Model for Monthly Rainfall Time-Series Forecasting Syaharuddin; Safaruddin; Vera Mandailina; Abdillah; Mahsup
Journal of Information System and Informatics Vol 8 No 4 (2026): August
Publisher : Asosiasi Doktor Sistem Informasi Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.63158/journalisi.v8i4.1693

Abstract

This study aimed to develop and evaluate a hybrid forecasting model integrating Ant Colony Optimization (ACO), Backpropagation Neural Network (BPNN), and XGBoost for monthly rainfall prediction. The proposed hybrid framework combines optimization, neural network, and boosting techniques within a single forecasting model. Monthly rainfall time-series data from 2016 to 2025 in Alas Subdistrict, Sumbawa Regency, West Nusa Tenggara, were used, comprising 120 observations obtained from BPS, BMKG, and NASA POWER. The methodology included data preprocessing, an 80%–20% chronological training–testing split, model development, and performance evaluation using MSE, MAE, RMSE, MAPE, and R². The results indicated that all models experienced performance degradation during testing, suggesting overfitting and limited generalization capability. The testing RMSE values for ACO, BPNN, XGBoost, and the hybrid model were 108.41, 109.33, 109.21, and 106.08 mm, respectively. The corresponding testing MAPE values were 2836.5%, 2900.5%, 2073.9%, and 2602.2%, although these values should be interpreted cautiously because rainfall observations occasionally approached zero. While the hybrid model achieved the lowest testing RMSE, the improvement over the best individual model was modest, and all testing R² values remained negative, indicating weak generalization capability. Therefore, the findings should be regarded as preliminary, and further validation using larger datasets, exogenous climatic predictors, baseline forecasting methods, and more rigorous evaluation procedures is required.
Co-Authors Abdillah Hendi Hidayah Mahsup Mahsup Mahsup Saba Mehmood Safaruddin Vera Mandailina Wasim Raza