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Journal : Bandung Conference Series: Mathematics

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Perbandingan Kompuatasi Numerik pada Interpolasi Spline Kubik Terapit dan Periodik 10060221015, Oktavia Nurmalinda; Yani Ramdani; Respitawulan
Bandung Conference Series: Mathematics Vol. 6 No. 1 (2026): Vol. 6 No. 1 (2026): Bandung Conference Series: Mathematics
Publisher : UNISBA Press

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29313/bcsm.v6i1.23120

Abstract

Abstract. Interpolation plays a vital role in various fields such as natural phenomenon modeling and engineering, yet the use of high-degree polynomials often leads to the Runge phenomenon. This study aims to analyze the comparison of formulation, curve visualization, and accuracy levels between Clamped Cubic Spline and Periodic Cubic Spline interpolation methods. The research method employed is quantitative with a numerical analysis approach using the test function over the interval [-1, 1]. The results indicate that the Clamped Cubic Spline provides a more stable and accurate approximation, with a true error of 0.00390625 at point x = -0.75. In contrast, the Periodic Cubic Spline produced a larger error of 0.02649, as the periodic condition forced the curve to follow properties not inherent in the non-periodic function. In conclusion, the choice of spline type must be adapted to the data characteristics, where the Clamped Spline is superior for data with known endpoint derivative information. Abstrak. Interpolasi berperan penting dalam berbagai bidang seperti pemodelan fenomena alam dan rekayasa, namun penggunaan polinomial derajat tinggi sering kali menimbulkan fenomena Runge. Penelitian ini bertujuan untuk menganalisis perbandingan formulasi, visualisasi kurva, dan tingkat akurasi antara metode interpolasi Spline Kubik Terapit (clamped) dan Spline Kubik Periodik. Metode penelitian yang digunakan adalah kuantitatif dengan pendekatan analisis numerik menggunakan fungsi uji pada interval [-1, 1]. Hasil penelitian menunjukkan bahwa Spline Kubik Terapit menghasilkan aproksimasi yang lebih stabil dan akurat dengan galat sejati sebesar 0,00390625 pada titik x = -0,75. Sebaliknya, Spline Kubik Periodik menghasilkan galat yang lebih besar, yaitu 0,02649, karena kondisi periodik memaksa kurva mengikuti sifat yang tidak dimiliki oleh fungsi non-periodik tersebut. Kesimpulannya, pemilihan jenis spline harus disesuaikan dengan karakteristik data, di mana Spline Terapit lebih unggul untuk data dengan informasi turunan ujung yang diketahui.
Co-Authors 10060221015, Oktavia Nurmalinda Aning Sofyan Sadikin Atie Rachmiatie Kusuma Wardhani, Aulya Lichandra, Funny Monica, Diva Neni Yulianita Sophia Novita Tresna Wiwitan Yani Ramdani