Strong asymptotics in Lagrange interpolation with equidistant nodes Original Research Article

In this paper we prove three conjectures of Revers on Lagrange interpolation for fλ(t)=|t|λ,λ>0, at equidistant nodes. In particular, we describe the rate of divergence of the Lagrange interpolants LN( fλ,t) for 0<|t|<1, and discuss their convergence at t=0. We also establish an asymptotic relation for max|t|⩽1| |t|λ−LN( fλ,t)|. The proofs are based on strong asymptotics for |t|λ−LN( fλ,t), 0⩽|t|<1.