Find polynomials, evaluate points, and visualize interpolation
Enter data points to find the unique polynomial passing through all points
| # | x | y = f(x) |
|---|
Minimum 2 points required. X values must be unique.
Calculate P(x) values for specific x coordinates
View the individual Li(x) polynomials that form the interpolation
Explore the polynomial with customizable chart settings
Formulas, properties, and theoretical background
For n+1 distinct points, there exists exactly one polynomial of degree at most n passing through all points.
The polynomial exactly passes through all given data points: P(xi) = yi for all i.
For n+1 points, the interpolating polynomial has degree at most n (may be less if points are collinear, etc.).
for some ξ in the interval containing x and all xi
High-degree polynomial interpolation on equally spaced points can produce oscillations near the interval edges. Use Chebyshev nodes for better results.
A method to find the unique polynomial of lowest degree passing through a given set of points.
Constructs basis polynomials that are 1 at one point and 0 at all others.
While elegant, direct Lagrange form has considerations.