12 research outputs found
Direct and Inverse Computation of Jacobi Matrices of Infinite Homogeneous Affine I.F.S
We introduce a new set of algorithms to compute Jacobi matrices associated
with measures generated by infinite systems of iterated functions. We
demonstrate their relevance in the study of theoretical problems, such as the
continuity of these measures and the logarithmic capacity of their support.
Since our approach is based on a reversible transformation between pairs of
Jacobi matrices, we also discuss its application to an inverse / approximation
problem. Numerical experiments show that the proposed algorithms are stable and
can reliably compute Jacobi matrices of large order.Comment: 20 pages 6 figure