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

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

2011-06-24

arxiv.org/abs/1106.4945v1

Mathematics

Numerical Analysis

20 pages 6 figures

Scientific paper

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.

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