Lagrange Interpolation Function and Cubic Spline Interpolation Function Implementation

This article presents a MATLAB program that implements both Lagrange interpolation and cubic spline interpolation functions. The program accepts an input vector containing x-values and a corresponding y-value vector, generating visual representations of the interpolated functions. The implementation includes two main algorithmic approaches: Lagrange interpolation using polynomial basis functions that pass exactly through all data points, and cubic spline interpolation that constructs piecewise cubic polynomials with continuous first and second derivatives at the nodes. Key MATLAB functions utilized in this implementation may include: - Polynomial evaluation and construction for Lagrange interpolation - Linear system solving for spline coefficient determination - Plotting functions for visualization of interpolated curves This program serves as a practical tool for better understanding and analyzing given datasets, enabling improved prediction and inference capabilities through mathematical interpolation techniques. The visualization component helps users observe how different interpolation methods handle data fitting and curve smoothing.