Interpolation Basics

Interpolation estimates values between known data points by fitting a curve, useful for smooth approximations.

Linear Interpolation

Given points \((x_0, y_0)\) and \((x_1, y_1)\), the value at \(x\) is \(y = y_0 + \frac{(y_1 - y_0)(x - x_0)}{x_1 - x_0}\).

Examples

For points (0, 0) and (2, 4), at \(x = 1\), linear interpolation gives \(y = 2\).

Advanced Methods

Lagrange polynomials and cubic splines offer higher accuracy for complex data.