Interpolation Theory

Interpolation Theory studies methods for constructing new data points within a set of known points, often used to estimate values between measurements. Imagine having a few weather readings and wanting to predict the temperature at a time between those measurements; interpolation methods create smooth, reliable estimates based on existing data. It ensures the estimated values fit well within the known data's structure, balancing accuracy and consistency. This theory applies across fields like mathematics, computer graphics, signal processing, and engineering, providing tools to fill in gaps or create continuous functions from discrete data points effectively.