https://doi.org/10.65770/KQGH6710
ABSTRACT
This study aims to compare Cubic Spline and PCHIP using the Chebyshev norm to construct a projection of household PLN electricity access in Indonesia for 2026. The data used in this study consist of the percentage of households using PLN electricity by province during the 2010-2025 period, obtained from Statistics Indonesia, with 33 provinces having complete time series data. The research method includes analytical function testing, construction of Cubic Spline and PCHIP interpolation functions, calculation of 2026 projections, and evaluation of the Chebyshev norm over the 2025-2026 interval. The main trajectory method is determined based on the smaller maximum function value over this interval. The results show that the average household access to PLN electricity increased from 77.92% in 2010 to 97.60% in 2025, while the standard deviation decreased from 17.01 to 3.44. The 2026 projection indicates that most provinces are already at a high level of electricity access, whereas West Papua, Papua, Central Kalimantan, East Nusa Tenggara, and West Kalimantan remain relatively lower. Based on the Chebyshev norm, PCHIP becomes the main method in 13 provinces, Cubic Spline in 12 provinces, and 8 provinces are classified as comparable.
References
- [1] T. Sambodo And R. Novandra, “The State Of Energy Poverty In Indonesia And Its Impact On Welfare,” Energy Policy, Vol. 132, Pp. 113–121, Sep. 2019, Doi: 10.1016/J.Enpol.2019.05.029.
- [2] K. Saputri, L. D. Setyonugroho, And D. Hartono, “Exploring The Determinants Of Energy Poverty In Indonesia’s Households: Empirical Evidence From The 2015–2019 Susenas,” Humanit. Soc. Sci. Commun., Vol. 11, No. 1, Dec. 2024, Doi: 10.1057/S41599-023-02514-Z.
- [3] A. Fakhouri, B. Abughazaleh, And M. I. Sayyed, “Comparative Evaluation Of Cubic Spline, Akima, And Pchip Interpolation Methods For Predicting Radiation Shielding Parameters Of Heavy Metal Oxide Glasses,” Nuclear Engineering And Technology, Jun. 2026, Doi: 10.1016/J.Net.2026.104232.
- [4] A. Rabbath And D. Corriveau, “A Comparison Of Piecewise Cubic Hermite Interpolating Polynomials, Cubic Splines And Piecewise Linear Functions For The Approximation Of Projectile Aerodynamics,” Defence Technology, Vol. 15, No. 5, Pp. 741–757, Oct. 2019, Doi: 10.1016/J.Dt.2019.07.016.
- [5] A. Abdul Karim, M. A. Mohd Rosli, And M. I. Mohd Mustafa, “Cubic Spline Interpolation For Petroleum Engineering Data,” Applied Mathematical Sciences, Vol. 8, No. 101–104, Pp. 5083–5098, 2014, Doi: 10.12988/Ams.2014.44284.
- [6] Jaffar, N. M. Thamrin, M. S. A. M. Ali, M. F. Misnan, A. I. M. Yassin, And N. M. Zan, “Spatial Interpolation Method Comparison For Physico-Chemical Parameters Of River Water In Klang River Using Matlab,” Bulletin Of Electrical Engineering And Informatics, Vol. 11, No. 4, Pp. 2368–2377, Aug. 2022, Doi: 10.11591/Eei.V11i4.3615.
- [7] Purwani, R. A. Hidayana, V. P. Balqis, And Sukono, “A Comparison Of Newton’s Divided Differences Interpolation And A Cubic Spline In Predicting The Poverty Rate Of West Java,” Engineering Letters, Vol. 31, No. 4, 2023.
- [8] Amat, Z. Li, J. Ruiz-Álvarez, C. Solano, And J. C. Trillo, “Adapting Cubic Hermite Splines To The Presence Of Singularities Through Correction Terms,” J. Sci. Comput., Vol. 95, No. 3, Jun. 2023, Doi: 10.1007/S10915-023-02191-9.
- [9] Kendall E. Atkinson And Weimin Han, Elementary Numerical Analysis, 3rd Ed. Hoboken, Nj, Usa: John Wiley & Sons, 2004.
- N. Fritsch And R. E. Carlson, “Monotone Piecewise Cubic Interpolation,” SIAM Journal on Numerical Analysis, vol. 17, no. 2, pp. 238–246, 1980, doi: 10.1137/0717021.
- Fan, P. Zhang, J. Chen, B. Li, L. Han, And Y. Zhou, “Quantitative Estimation Of Missing Value Interpolation Methods For Suomi-Npp Viirs/Dnb Nighttime Light Monthly Composite Images,” Ieee Access, Vol. 8, Pp. 199266–199288, 2020, Doi: 10.1109/Access.2020.3035408.
- Cao, X. Li, S. Belabbes, L. Dell’oro, And C. Dou, “Estimates Of Power Supply During The 2023 Gaza Humanitarian Crisis Using Night-Time Light Images,” Geo-Spatial Information Science, 2025, Doi: 10.1080/10095020.2024.2439387.
- Pan Et Al., “Modis Daily Cloud-Gap-Filled Fractional Snow Cover Dataset Of The Asian Water Tower Region (2000-2022),” Earth Syst. Sci. Data, Vol. 16, No. 5, Pp. 2501–2523, May 2024, Doi: 10.5194/Essd-16-2501-2024.
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