Computing the Hessenberg matrix associated with a self-similar measure

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.

Description

Title: Computing the Hessenberg matrix associated with a self-similar measure
Author/s:
  • Escribano Iglesias, M. del Carmen
  • Giraldo Carbajo, Antonio
  • Sastre Rosa, María de la Asunción
  • Torrano Gimenez, Emilio
Item Type: Article
Título de Revista/Publicación: Journal of Approximation Theory
Date: January 2011
ISSN: 0021-9045
Volume: 163
Subjects:
Freetext Keywords: Self-similar measures; Orthogonal polynomials; Moment matrix; Hessenberg matrix
Faculty: Facultad de Informática (UPM)
Department: Matemática Aplicada
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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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.

More information

Item ID: 12370
DC Identifier: http://oa.upm.es/12370/
OAI Identifier: oai:oa.upm.es:12370
DOI: 10.1016/j.jat.2010.02.008
Deposited by: Memoria Investigacion
Deposited on: 17 Aug 2012 12:07
Last Modified: 10 Apr 2019 14:00
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