The anti-triangular factorization of symmetric matrices (Articolo in rivista)

Type
Label
  • The anti-triangular factorization of symmetric matrices (Articolo in rivista) (literal)
Anno
  • 2013-01-01T00:00:00+01:00 (literal)
Alternative label
  • Mastronardi Nicola; Van Dooren Paul (2013)
    The anti-triangular factorization of symmetric matrices
    in SIAM journal on matrix analysis and applications (Print)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Mastronardi Nicola; Van Dooren Paul (literal)
Rivista
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Istituto per le Applicazioni del Calcolo ``M. Picone'', sede di Bari, Consiglio Nazionale delle Ricerche, Via G. Amendola, 122/D, I-70126 Bari, Italy. Department of Mathematical Engineering, Catholic University of Louvain, Batiment Euler, Avenue Georges Lemaitre 4, B-1348 Louvain-la-Neuve, Belgium. (literal)
Titolo
  • The anti-triangular factorization of symmetric matrices (literal)
Abstract
  • Indefinite symmetric matrices occur in many applications, such as optimization, least squares problems, partial differential equations and variational problems. In these applications one is often interested in computing a factorization of the indefinite matrix that puts into evidence the inertia of the matrix or possibly provides an estimate of its eigenvalues. In this paper we propose an algorithm that provides this information for any symmetric indefinite matrix by transforming it to a block anti-triangular form using orthogonal similarity transformations. We also show that the algorithm is backward stable and has a complexity that is comparable to existing matrix decompositions for dense indefinite matrices. (literal)
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