Interpolation with respect to random points

Abstract

In [1] we discussed the problem of constructing cubic interpolation formulae with random nodes and gave the distribution function of these nodes. We also calculated the dispersion of the random variable defined by the cubic interpolation formula and showed that under certain conditions it tends to zero as the number of nodes increases. We shall now discuss the problem of interpolation with random nodes which are distributed according to the same law as in [1], and in one special case we indicate a simple numerical procedure for carrying out the random process both for interpolation and for the calculation of an integral.