Approximate interpolation by functions in a Haar space (Q909164)

Let \(\{\phi_ 1,...,\phi_ n\}\) be a Chebyshev system in C(I), where I is a proper compact interval in R. In J. Approximation Theory 32, 257-270 (1981; Zbl 0472.41024)] the author proved that interpolation process can be performed approximately, with error at most \(\epsilon\), on a set of \(n+1\) distinct points of I, provided that set is sufficiently close to degenerating into an n-point one. The propose of this paper is to show how that approximate interpolation result can be substantially improved.