Our interpolation calculator uses proven numerical methods to estimate values between known data points. The process involves constructing polynomials that pass through your data points and evaluating them at the target location. Each method offers different advantages for various types of data and accuracy requirements.

Mathematical Foundation

Interpolation is based on the Weierstrass approximation theorem, which states that any continuous function can be uniformly approximated by polynomials. Each method constructs a unique polynomial of degree n-1 that passes through n data points, providing different computational advantages and numerical properties.

• Linear interpolation provides first-order accuracy with minimal computation
• Lagrange method offers explicit polynomial form but can be numerically unstable
• Newton's divided differences allow efficient addition of new data points
• Higher-degree polynomials can suffer from Runge's phenomenon with many points

Sources & References