ABSTRACT
This study aims to compare the effectiveness of the Cubic Spline and the Near Minimax Approximation method in approximating non-linear functions. Observational or experimental results are often represented in the form of non-linear functions, requiring numerical approaches to construct mathematical models that can approximate these functions. The Cubic Spline is used to produce smooth approximation functions with the advantage of preserving the original data’s shape, while the Near Minimax Approximation method focuses on minimizing the maximum error between the approximated function and the original function, thereby achieving stability in maximum error across the domain. The results of the study indicate that the Near Minimax Approximation method outperforms in producing a more uniform error distribution and smaller maximum error values compared to the Cubic Spline. This method demonstrates excellent performance in high-degree interpolation, with significantly lower maximum errors compared to the Newton method at the same degree. Meanwhile, the Cubic Spline excels in generating smooth curves and is well-suited for data with evenly distributed points.
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