A stable stieltjes technique for computing orthogonal polynomials and jacobi matrices associated with a class of singular measures

A recursive technique for the determination of Jacobi matrices associated with multifractal measures generated by Iterated Function Systems is described. This technique allows for the stable determination of large-rank matrices, a task for which the conventional approach, classical polynomial sampling, is proven here to be severely ill-conditioned. Application to the integration of smooth functions is presented in a physical example, and relevance of this new technique to the study of the asymptotic properties of orthogonal polynomials of singular measures is discussed. Further applications to the study of almost periodic quantum systems are briefly mentioned.