The authors present a systematic method of approximating, to an arbitrary accuracy, a probability measure μ on x=[0,1]’q, q≥1, with invariant measures for iterated function systems by matching its moments. There are two novel features in the treatment. 1. An infinite set of fixed affine contraction maps on X, 𝒲={w1,w2,...}, subject to an ‘∈-contractivity’ condition, is employed. Thus, only an optimization over th associated probabilities pi is required. 2. The authors prove a collage theorem for moments which reduces the moment matching problem to that of minimizing the collage distance between moment vectors. The minimization procedure is a standard quadratic programming problem in the pi which can be solved in a finite number of steps. Some numerical calculations for the approximation of measures on [0,1] are presented.
