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2016 | 4 | 1 | 13-30
Tytuł artykułu

Pentadiagonal Companion Matrices

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The class of sparse companion matrices was recently characterized in terms of unit Hessenberg matrices. We determine which sparse companion matrices have the lowest bandwidth, that is, we characterize which sparse companion matrices are permutationally similar to a pentadiagonal matrix and describe how to find the permutation involved. In the process, we determine which of the Fiedler companion matrices are permutationally similar to a pentadiagonal matrix. We also describe how to find a Fiedler factorization, up to transpose, given only its corner entries.
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
1
Strony
13-30
Opis fizyczny
Daty
wydano
2016-01-01
otrzymano
2015-07-27
zaakceptowano
2015-10-28
online
2015-12-16
Twórcy
  • Department of Mathematics, Redeemer University College, 777 Garner Rd E, L9K 1J4 Ancaster, Canada, beastman@redeemer.ca
  • Department of Mathematics, Redeemer University College, 777 Garner Rd E, L9K 1J4 Ancaster, Canada, kvanderm@redeemer.ca
Bibliografia
  • [1] J.L. Aurentz, R. Vandebril, and D.S. Watkins, Fast computation of the zeros of a polynomial via factorization of the companion matrix, SIAM J. Sci. Comput.35 (2013) A255 – A269.[WoS]
  • [2] J.L. Aurentz, R. Vandebril, and D.S. Watkins, Fast computation of eigenvalues of companion, comrade, and related matrices, BIT Numer. Math.54 (2014) 7–30.
  • [3] T. Bella, V. Olshevsky, and P. Zhlobich, A quasiseparable approach to five-diagonal CMV and Fiedler matrices, Linear Algebra Appl.434(4) (2011) 957–976.[WoS]
  • [4] B. Bevilacqua, G.M. Del Corso, and L. Gemignani, A CMV–based eigensolver for companion matrices, SIAM J. Matrix Anal. Appl.36(3) (2015) 1046–1068.[WoS][Crossref]
  • [5] D.A. Bini, P. Boito, Y. Eidelman, L. Gemignani, and I. Gohberg, A fast implicit QR eigenvalue algorithm for companion matrices, Linear Algebra Appl.432(8) (2010) 2006–2031.[WoS]
  • [6] D.A. Bini, F. Daddi, and L. Gemignani, On the shifted QR iteration applied to companion matrices, Electron. Trans. Numer. Anal.18 (2004) 137–152.
  • [7] S. Chandrasekaran, M. Gu, J. Xia, and J. Zhu, A fast QR algorithm for companion matrices, Oper. Theory Adv. Appl.179 (2008) 111–143.
  • [8] F. De Terán, F. Dopico, and D.S. Mackey, Fiedler companion linearizations and the recovery of minimal indices, SIAM J. Matrix Anal. Appl., 31:4 (2010) 2181–2204.[WoS][Crossref]
  • [9] F. De Terán, F. Dopico, and J. Pérez, Condition numbers for inversion of Fiedler companion matrices, Linear Algebra Appl.439 (2013) 944–981.[WoS]
  • [10] B. Eastman, I.-J. Kim, B. Shader, and K.N. Vander Meulen, Companion matrix patterns, Linear Algebra Appl.463 (2014) 255–272.[WoS]
  • [11] M. Fiedler, A note on companion matrices, Linear Algebra Appl.372 (2003) 325–331.
  • [12] C. Garnett, B. Shader, C. Shader, and P. van den Driessche, Characterization of a family of generalized companion matrices Linear Algebra Appl. (2015), in press, .[Crossref]
  • [13] N.J. Higham, D.S. Mackey, N. Mackey, and F. Tisseur, Symmetric linearizations for matrix polynomials, SIAM J. Matrix Anal. Appl.29 (2006) 143–159.[WoS]
  • [14] C. Ma and X. Zhan, Extremal sparsity of the companion matrix of a polynomial, Linear Algebra Appl.438 (2013) 621–625.[WoS]
  • [15] S. Vologiannidis and E.N. Antoniou, A permuted factors approach for the linearization of polynomial matrices, Math. Control Signals Systems22 (2011) 317–342.[WoS]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2016-0003
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