Lagrange interpolation

Lagrange interpolation is a mathematical method used to find a smooth curve that passes exactly through a set of known points. Imagine you have several data points, each with an x (independent variable) and y (dependent variable). Lagrange interpolation constructs a single polynomial function by combining specific formulas called basis polynomials, each designed to be zero at all points except one. When summed, these basis polynomials produce a curve that matches all given points exactly, allowing you to estimate values between or beyond these points with confidence in the polynomial’s accuracy at those known points.