Inverses of regular Hessenberg matrices

Abderramán Marrero, Jesús Carmelo and Tomeo Perucha, Venancio (2010). Inverses of regular Hessenberg matrices. In: "10th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2010", 27/06/2010 - 30/06/2010, Almeria, España.

Description

Title: Inverses of regular Hessenberg matrices
Author/s:
  • Abderramán Marrero, Jesús Carmelo
  • Tomeo Perucha, Venancio
Item Type: Presentation at Congress or Conference (Article)
Event Title: 10th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2010
Event Dates: 27/06/2010 - 30/06/2010
Event Location: Almeria, España
Title of Book: Proceedings of the 10th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2010
Date: 2010
Subjects:
Freetext Keywords: General orthogonal polynomials, Hessenberg matrix, Hessenbergian, inverse matrix, lower semiseparable (plus diagonal) matrix, resolvent matrix
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Matemática Aplicada a la Ingeniería Técnica de Telecomunicación [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

A new proof of the general representation for the entries of the inverse of any unreduced Hessenberg matrix of nite order is found. Also this formulation is extended to the inverses of reduced Hessenberg matrices. Those entries are given with proper Hessenbergians from the original matrix. It justies both the use of linear recurrences for such computations and some elementary properties of the inverse matrix. As an application of current interest in the theory of orthogonal polynomials on the complex plane, the resolvent matrix associated to a nite Hes- senberg matrix in standard form is calculated. The results are illustrated with two examples on the unit disk.

More information

Item ID: 9285
DC Identifier: http://oa.upm.es/9285/
OAI Identifier: oai:oa.upm.es:9285
Official URL: http://gsii.usal.es/~CMMSE/index.php?option=com_content&task=view&id=15&Itemid=16
Deposited by: Memoria Investigacion
Deposited on: 13 Oct 2011 07:45
Last Modified: 20 Apr 2016 17:46
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