Observatorio de I+D+i UPM

Memorias de investigación
Book chapters:
An extension of the Ikebe algorithm for the inversion of
Year:2012
Research Areas
  • Physics chemical and mathematical,
  • Mathematics,
  • Sciences of the computation: symbolic and formal calculus
Information
Abstract
Ikebe algorithm for computing the lower half of the inverse of any (unreduced) upper Hessenberg matrix is extended here to compute the entries of the superdiagonal. It gives rise to an algorithm of inversion based on the factorization H?1 = HL ?U?1. The lower Hessenberg matrix HL is a quasiseparable one and U?1 is upper triangular, with diagonal entries ui;i = 1. Its computational complexity, O(n3), is connected with back substitution for the inversion of the matrix U. Moreover, the inverses of quasiseparable Hessenberg matrices are obtained in O(n2) times. Numerical comparisons with other specialized algorithms of inversion are also introduced.
International
Si
Book Edition
Book Publishing
ISBN
978-84-615-5392-1
Series
Book title
Proceedings of the 12th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2012
From page
23
To page
26
Participants
  • Autor: Venancio Tomeo Perucha (UPM)
  • Autor: Jesus Carmelo Abderraman Marrero (UPM)
Research Group, Departaments and Institutes related
  • Creador: Grupo de Investigación: Polinomios Ortogonales y Geometría Fractal
  • Departamento: Matemática Aplicada (Facultad de Informática)
  • Departamento: Matemática Aplicada a las Tecnologías de la Información
S2i 2019 Observatorio de investigación @ UPM con la colaboración del Consejo Social UPM
Cofinanciación del MINECO en el marco del Programa INNCIDE 2011 (OTR-2011-0236)
Cofinanciación del MINECO en el marco del Programa INNPACTO (IPT-020000-2010-22)