Lagrange polynomial

A Lagrange polynomial is a mathematical tool used to find a smooth curve that exactly passes through a given set of points. Imagine plotting a few dots on a graph; the Lagrange polynomial creates a single, continuous curve connecting all these dots without deviating from them. It does this by constructing special functions (basis polynomials) for each point, which are combined to form the overall polynomial. This method helps in interpolating data, predicting values, and understanding relationships between points in various scientific and engineering applications.