Citation
Escribano Iglesias, M. del Carmen and Giraldo Carbajo, Antonio and Sastre Rosa, María de la Asunción and Torrano Gimenez, Emilio
(2011).
Computing the Hessenberg matrix associated with a self-similar measure.
"Journal of Approximation Theory", v. 163
(n. 1);
pp. 49-64.
ISSN 0021-9045.
https://doi.org/10.1016/j.jat.2010.02.008.
Abstract
We introduce in this paper a method to calculate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calculate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures.
We apply this method to approximate the Hessenberg matrix associated with a self-similar measure and compare it with the result obtained by a former method for self-similar measures which uses a fixed point theorem for moment matrices. Results are given for a series of classical examples of self-similar measures.
Finally, we also apply the method introduced in this paper to some examples of sums of (not self-similar) measures obtaining the exact value of the sections of the Hessenberg matrix.
