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CHAPTER 4

Newton Interpolation and Difference Triangles

We are going to revisit polynomial interpolation one more time. So far we have encountered several important polynomial bases, including

Monomial basis: 1,t,…, tⁿ

Taylor basis: 1,(t − t₀),…, (t − t₀)ⁿ

Lagrange basis: Lⁿ₀(t | t₀,…, t_n),…, Lⁿ_n(t | t₀,…, t_n)

Hermite basis: H₀(t | t₀, t₀,…,

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