Direct and Inverse Computation of Jacobi Matrices of Infinite Homogeneous Affine I.F.S

TL;DR

This paper presents new algorithms for computing Jacobi matrices related to measures from infinite iterated function systems, with applications in measure continuity, capacity, and inverse problems, supported by stable numerical experiments.

Contribution

The paper introduces a reversible transformation-based approach for direct and inverse computation of Jacobi matrices in infinite I.F.S., advancing theoretical and numerical analysis.

Findings

Algorithms are stable and reliable for large matrices

Applications include measure continuity and capacity analysis

Effective in inverse and approximation problems

Abstract

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.