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We present a new stability analysis for the second barycentric formula, showing that this formula is backward stable when the relevant Lebesgue constant is small.
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)
In the recent paper “On certain Vandermonde determinants whose variables separate” [Linear Algebra and its Applications 449 (2014) pp. 17–27], there was established a factorized formula for some bivariate Vandermonde determinants (associated to almost square grids) whose basis functions are formed by Hadamard products of some univariate polynomials. That… (More)
In this note we present a broad comparison between trigonometric interpolation and a specific version of extended Floater–Hormann interpolants which is accurate and stable for the interpolation of periodic functions at equally spaced nodes. The conclusion is that both techniques are equivalent in practice.