CUBIC SPLINE INTERPOLATION TO APPROXIMATE SEA DEPTH BETWEEN TELUK SUAK AND LEMUKUTAN ISLAND
Abstract
Interpolation is a technique that determines the value of a function at a point located between several known data points. Various interpolation methods include polynomial interpolation, Lagrange interpolation, Newton interpolation, and spline interpolation. Cubic spline interpolation aims to produce accurate approximations characterized by minimal oscillations in the resulting curve. This research uses the cubic spline interpolation method to estimate the sea depth in the waters between Teluk Suak and Pulau Lemukutan. The sea depth measurements are conducted to acquire information regarding the underwater topography. We collected data points using remote sensing techniques through Google Earth Pro. These points are selected based on the sea depth profile considerations, including steep areas and points of depth variation to maintain the seabed conditions within the interpolation curve, with a total of 31 data points. Subsequently, we subjected these data points to the conditions necessary for cubic spline interpolation, resulting in a system of 120 linear equations. After solving this system of linear equations, we obtained cubic spline interpolation polynomials for each subinterval and then estimated the sea depth at other points. Based on the cubic spline interpolation results, we achieved a Mean Average Percentage Error (MAPE) of 1.58%, indicating a highly accurate interpolation outcome.
Keywords
Full Text:
PDFReferences
Burden, R. L., & Faires, J. D. (2010). Numerical Analysis (9 ed.). Richard Stratton.
Chikwendu, C. R., Oduwole, H. K., & Okoro, S. I. (2015). An Application of Spline and Piecewise Interpolation to Heat Transfer (Cubic Case). Mathematical Theory and Modeling, 5(6), 28–39.
Epperson, J. F. (2013). An Introduction to Numerical Methods and Analysis (7 ed.). John Wiley & Sons, Inc.
Erfianto, B., & Setiawan, A. H. (2020). Interpolasi Cubic Spline untuk Memetakan Distribusi Panas pada Permukaan Panel Sel Surya. ELKOMIKA: Jurnal Teknik Energi Elektrik, Teknik Telekomunikasi, & Teknik Elektronika, 8(3), 467. https://doi.org/10.26760/elkomika.v8i3.467
Gandha, G. I. (2021). The modelling of nonlinear distance sensor using piecewise newton polynomial with vertex algorithm. JURNAL INFOTEL, 13(3), 160–166. https://doi.org/10.20895/infotel.v13i3.678
Karim, A. S. A., Rosli, M. A. M., & Mustafa, M. I. M. (2014). Cubic spline interpolation for petroleum engineering data. Applied Mathematical Sciences, 8(102), 5083–5098. https://doi.org/10.12988/ams.2014.44284
Lewis, C. D. (1982). Industrial and Business Forecasting Methods: A Practical Guide to Exponential Smoothing and Curve Fitting. Butterworth Scientific. https://books.google.co.id/books?id=t8W4AAAAIAAJ
Pambuko, D. M., Umbara, R. F., & Telekomunikasi Terusan Buah Batu Bandung, J. (2013). Identifikasi Kedalaman Laut (Bathymetry) berdasarkan Warna Permukaan Laut pada Citra Satelit menggunakan Metode ANFIS (Vol. 9, Nomor 2).
Purwati, N. K. R., & Erawati, N. K. (2020). Pengantar Metode Numerik. Klik Media.
Roe, D. R., & Brooks, B. R. (2021). Improving the speed of volumetric density map generation via cubic spline interpolation. Journal of Molecular Graphics and Modelling, 104, 1–6. https://doi.org/10.1016/j.jmgm.2021.107832
Visca, A. S., Syafwan, M., & Putri, A. R. (2019). INTERPOLASI SPLIN KUBIK TERAPIT. Dalam Jurnal Matematika UNAND: Vol. VIII (Nomor 2).
DOI: https://doi.org/10.20527/epsilon.v18i1.10813
Refbacks
- There are currently no refbacks.
Copyright (c) 2024 EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN
Indexed by:
EDITORIAL OFFICE
All articles published in "Epsilon: Jurnal Matematika Murni dan Terapan" are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0). Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.