Theorems · Theorem · linear algebra

Lagrange.eval_interpolate_not_at_node

∀ {F : Type u_1} [inst : Field F] {ι : Type u_2} [inst_1 : DecidableEq ι] {s : Finset ι} {v : ι → F} (r : ι → F)
  {x : F},
  (∀ i ∈ s, x ≠ v i) →
    Polynomial.eval x ((Lagrange.interpolate s v) r) =
      Polynomial.eval x (Lagrange.nodal s v) * ∑ i ∈ s, Lagrange.nodalWeight s v i * (x - v i)⁻¹ * r i

This is the first barycentric form of the Lagrange interpolant.

Defined in

Mathlib.LinearAlgebra.Lagrange

Cited by

2 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldDecidableEq