Data Interpolation Using Polynomial Methods and Cubic Spline

This study aims to clarify the fundamental concepts of numerical analysis in general, followed by an exploration of interpolation principles. Interpolation is categorized into general and piecewise types. The research discusses several methods for general interpolation and the associated error formulas. It was found that interpolation using Lagrange, Newton’s forward and backward methods, and Hermite involves approximating data with polynomials that pass through all given points. As a result, the resulting polynomials tend to be of high degree, and such polynomials exhibit oscillatory behavior—the higher the degree, the greater the oscillation—which limits their practical use. Therefore, cubic spline interpolation is preferred to ensure continuity and smoothness in piecewise interpolation. The study examines the concept of cubic splines, their construction, types, and supports the discussion with examples and relevant theorems.