Some new results on Lagrange interpolation for bounded variation functions (Q979052)

In an earlier paper [Constructive Approximation 15, No. 2, 257--289 (1999; Zbl 0926.41001)], the present authors have proved that for every \(f\in C(-1,1)\) suitable matrices of nodes exist such that the corresponding sequence of Lagrange interpolating polynomials converges to \(f\) with order \(o(m^{-1/p})\) in some \(L^p\) weighted space, \(1<p<\infty\). In this paper the authors prove a similar result for \(f\in BV\) without requiring its continuity. Moreover the order of convergence is the best.