Akademik Veri Yönetim Sistemi
International Conference on Mathematics and Mathematics Education (ICMME-2024), Nevşehir, Türkiye, 3 - 05 Ekim 2024, ss.103-104
Interpolation is a fundamental mathematical technique used to estimate unknown values within the bounds of known data points. This presentation delves into five prominent interpolation methods: Linear Interpolation, Polynomial Interpolation, Spline Interpolation, Radial Basis Function (RBF) Interpolation, and Kriging Method, highlighting their applications, mathematical foundations, and relative strengths and weaknesses.
The Linear Interpolation method is the simplest among the five, offering a quick and straightforward solution by drawing a straight line between two known data points to estimate intermediate values. Its primary advantage lies in its computational efficiency, but it is limited in precision, especially for datasets that exhibit non-linear structures. Polynomial Interpolation, in contrast, fits a single polynomial to the entire dataset, offering more accuracy in capturing the underlying trend, particularly for small datasets. However, it is prone to significant errors, especially when using highdegree polynomials. Spline Interpolation overcomes some of the drawbacks of Polynomial Interpolation by using piecewise polynomials to ensure smooth transitions between data points. Particularly, cubic splines are favored for their balance between precision and computational complexity. Radial Basis Function (RBF) Interpolation is particularly effective for high-dimensional data and in scenarios where capturing intricate relationships between data points is crucial. The Kriging method is a geostatistical interpolation technique that excels in spatial data analysis.
The presentation also compares these methods using TOPSİS across four key criteria: precision, computation speed, flexibility, and error margin. Linear Interpolation, while fast, is the least precise. Polynomial Interpolation can be precise but risks high error margins with increasing polynomial degree. Spline Interpolation offers a good balance of precision and flexibility, while RBF Interpolation provides flexibility at the cost of computational speed. Kriging stands out for its low error margin despite requiring higher computation.
In conclusion, the choice of an interpolation method depends on the specific requirements of the task at hand, including the nature of the data, desired accuracy, and available computational resources. The purpose of this presentation is to provide a comprehensive understanding of the methods discussed and facilitate informed decision making in their application in various fields.