What is Interpolation Lagrange Calculator and Why it Matters?
Polynomial interpolation reconstructs a smooth function from discrete samples and is foundational in approximation theory.
Mathematical Formula and Theory
P(x)=Σ yᵢ ℓᵢ(x), ℓᵢ(x)=∏_{j≠i}(x−xⱼ)/(xᵢ−xⱼ). Unique of degree at most n−1.
How to Use This Calculator - Step by Step
- Enter data pairs and evaluation point.
- Click Interpolate.
Solved Example with Full Calculation
Points (0,1),(1,2),(2,0),(3,5). P(1.5)≈1.4375.