On the inverse problem of constructing symmetric pentadiagonal toeplitz matrices from three largest eigenvalues (Articolo in rivista)

Type
Label
  • On the inverse problem of constructing symmetric pentadiagonal toeplitz matrices from three largest eigenvalues (Articolo in rivista) (literal)
Anno
  • 2005-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1088/0266-5611/21/6/005 (literal)
Alternative label
  • Chu M.T.; Diele F.; Ragni S. (2005)
    On the inverse problem of constructing symmetric pentadiagonal toeplitz matrices from three largest eigenvalues
    in Inverse problems (Print)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Chu M.T.; Diele F.; Ragni S. (literal)
Pagina inizio
  • 1879 (literal)
Pagina fine
  • 1894 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://iopscience.iop.org/0266-5611/21/6/005 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 21 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 6 (literal)
Note
  • Scopu (literal)
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • CHU Moody T., North Carolina State University, USA DIELE Fasma, Istituto per le Applicazioni del Calcolo \"Mauro Picone\" RAGNI Stefania, Università degli Studi di Bari (literal)
Titolo
  • On the inverse problem of constructing symmetric pentadiagonal toeplitz matrices from three largest eigenvalues (literal)
Abstract
  • The inverse problem of constructing a symmetric Toeplitz matrix with prescribed eigenvalues has been a challenge both theoretically and computationally in the literature. It is now known in theory that symmetric Toeplitz matrices can have arbitrary real spectra. This paper addresses a similar problem--can the three largest eigenvalues of symmetric pentadiagonal Toeplitz matrices be arbitrary? Given three real numbers ? ? ? ? ?, this paper finds that the ratio ? = ?-? ?-? , including infinity if ? = ?, determines whether there is a symmetric pentadiagonal Toeplitz matrix with ?, ? and ? as its three largest eigenvalues. It is shown that such a matrix of size n × n does not exist if n is even and ? is too large or if n is odd and ? is too close to 1. When such a matrix does exist, a numerical method is proposed for the construction. (literal)
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