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It is known that the Lagrange interpolation problem at equidistant nodes isill-conditioned. We explore the influence of the interval length in thecomputation of divided differences of the Newton interpolation formula.Condition numbers are computed for lower triangular matrices associated to theNewton interpolation formula at equidistant nodes. We consider the collocationmatrices $L$ and $P_L$ of the monic Newton basis and a normalized Newton basis,so that $P_L$ is the lower triangular Pascal matrix. In contrast to $L$, $P_L$does not depend on the interval length, and we show that the Skeel conditionnumber of the $(n+1)\times (n+1)$ lower triangular Pascal matrix is $3^n$. The$\infty$-norm condition number of the collocation matrix $L$ of the monicNewton basis is computed in terms of the interval length. The minimumasymptotic growth rate is achieved for intervals of length 3.

Optimal interval length for the collocation of the Newton basis