Notes on Lagrange Interpolating Polynomials

7 hours ago

Polynomial interpolation finds a polynomial that fits a set of distinct points perfectly.
The Vandermonde matrix is used to solve for polynomial coefficients but is often ill-conditioned.
Lagrange interpolation polynomials use basis functions that are 1 at their node and 0 at others.
The Lagrange basis functions form a linear algebra basis for the vector space of polynomials.
The interpolating polynomial is unique and of degree at most n-1 for n distinct points.
The Vandermonde matrix is invertible when nodes are distinct, proven via its determinant.

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