Direct and Inverse Computation of Jacobi Matrices of Infinite Homogeneous Affine I.F.S
Provides computational tools for theoretical analysis of fractal measures, but the contribution is incremental as it extends existing methods to infinite systems.
The paper introduces algorithms for computing Jacobi matrices of measures from infinite iterated function systems, demonstrating stability and reliability for large orders, with applications to continuity and capacity problems.
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.