ON RATIONAL INTERPOLATION TO VERTICAL-BAR-X-VERTICAL-BAR AT THE ADJUSTED CHEBYSHEV NODES

Recently Brutman and Passow considered Newman-type rational interpolat ion to \x\ induced by arbitrary sets of symmetric nodes in [ -1, 1] an d showed that under mild restrictions on the location of the interpola tion nodes, the corresponding sequence of rational interpolants conver ges to \x\ They also studied the special case where the interpolation nodes are the roots of the Chebyshev polynomials and proved that for t his case the exact order of approximation is O(1/n log n), which, in v iew of Werner's result, is the same as for rational interpolation at e quidistant nodes. In the present note we consider the set of interpola tion nodes obtained by adjusting the Chebyshev roots to the interval [ 0, 1] and then extending this set to [ -1, I] in a symmetric way. We s how that this procedure improves the quality of approximation, namely we prove that in this ease the exact order of approximation is O(1/n(2 )). (C) 1998 Academic Press.