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In this note we extend the definition of the first barycentric formula for Lagrange interpolation to Floater-Hormann interpolants and present an algorithm to evaluate it which is backward stable on the entire real line. We also discuss in detail the numerical stability of the second barycentric formula for Floater-Hormann interpolants.
In the statement of Theorem 2 of , replace (Z + 1))(x, μ(x)) < 1 by Z(1 + (x, μ(x))) < 1. The numbers 2δ and 2.24δ in equations (26) and (28), Lemma 2 of , must be replaced by 4δ and 4.45δ, respectively, as we shall explain below. In the equation (42) of the proof of Lemma 2 of we have ζ(x, x) i,j ≤ 2δ η(x) j +d τ = j τ = i 1 |i−τ | ≤ 2δ η(x) [1 +… (More)