Some more general bounds on the residual term of the Lagrange interpolation formula

Error bounds are derived for the Lagrange interpolation formula and for the k-th derivative of the residual term of this formula in terms of the Lipschitz constant of the n-th derivative for the case with (n+1) nodes and also for the case when the functions satisfy a special condition: G x, y, z a, b]: ¦ (x)(z–y) +(y)(x–z)+(z)(y–x)¦G¦(x–y)(y–z)(z–x)¦.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 73, pp. 27–32, 1992.