RECONSTRUCTION OF A FUNCTION USING NODE POINTS SPLINE INTERPOLATION

Abstract

Spline interpolation is one of the most effective numerical methods for reconstructing functions based on discrete data points. In many scientific and engineering applications, the exact analytical form of a function is unknown, and only its values at certain nodes are available. In such cases, interpolation methods are used to approximate the function. However, high-degree polynomial interpolation often leads to oscillations known as the Runge phenomenon, which decreases the accuracy of approximation. This study focuses on the theory and application of cubic spline interpolation for reconstructing functions from node points. The mathematical model of the cubic spline method is described, and the system of linear equations required to determine the spline coefficients is derived. The computational algorithm for solving the problem using the Thomas method for tridiagonal matrices is also presented. The results demonstrate that spline interpolation provides a smooth and accurate approximation of functions while avoiding oscillations typical for high-degree polynomial interpolation.