The numerical stability of barycentric Lagrange interpolation

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Six myths of polynomial interpolation and quadrature (2011, result): “The work required is O(n) per evaluation point, and though the divisions by x− xj may look dangerous for x ≈ xj , the formula is numerically stable, as was proved by Nick Higham in 2004 [6].”
Barycentric rational interpolation with no poles and high rates of approximation (2007, background): “We also note that Higham [14] has shown that if the Lebesgue constant is small, Lagrange polynomial interpolation using the”
Linearization of matrix polynomials expressed in polynomial bases (2008, background): “The paper is organised accordingly: Sections 2 and 3 are concerned with degree-graded bases.”
The spectra of gravitational atoms (2019, background): “J C A P 1 2 ( 2 0 1 9 ) 0 0 6 is numerically robust [57, 59] and computationally efficient.”
Rectangular spectral collocation (2015, methodology): “…piecewise smooth solutions, they offer rapid convergence (typically exponential) in the number of degrees of freedom, and can be used in conjunction with asymptotically fast and stable algorithms such as the FFT and barycentric interpolation formula of Berrut & Trefethen (2004) and Higham (2004).”
A spectral element approach for the stability of delay systems (2011, methodology): “In agreement with Reference [55], a more effective representation of Lagrange polynomials is provided by the barycentric formula according to”