181
Views
4
CrossRef citations to date
0
Altmetric
Articles

Inverses of generalized Hessenberg matrices

&
Pages 559-570 | Received 05 Feb 2013, Accepted 30 Dec 2013, Published online: 05 Mar 2014

References

  • Bevilaqua R, Bozzo E, Del Corso GM. qd-Type methods for quasiseparable matrices. SIAM J. Matrix Anal. Appl. 2011;32:722–747.
  • Vandebril R, Van Barel M, Mastronardi N. Matrix computations and semiseparable matrices. Vol. 1, Linear systems. Baltimore (MD): Johns Hopkins University Press; 2008.
  • Asplund E. Inverses of matrices aij which satisfy aij = 0 for j > i + p. Math. Scand. 1959;7:57–60.
  • Elsner L. Some observations on inverses of band matrices and low rank perturbations of triangular matrices. Acta Technica Acad. Sci. Hung. 1999;108:41–48.
  • Fiedler M, Markham TL. Completing a matrix when certain entries of its inverse are specified. Linear Algebra Appl. 1986;74:225–237.
  • Gustafson WH. A note on matrix inversion. Linear Algebra Appl. 1984;57:71–73.
  • Chandrasekaran S, Gu M. Fast and stable algorithms for banded plus semiseparable systems of linear equations. SIAM J. Matrix Anal. Appl. 2003;25:373–384.
  • Stewart GW. Updating a rank-revealing ULV decomposition. SIAM J. Matrix Anal. Appl. 1993;14:494–499.
  • Cao WL, Stewart WJ. A note on inverses of Hessenberg-like matrices. Linear Algebra Appl. 1986;76:233–240.
  • Faddeev DK. Properties of a matrix, inverse of a Hessenberg matrix. J. Math. Sci. 1984;24:118–120.
  • Ikebe Y. On inverses of Hessenberg matrices. Linear Algebra Appl. 1979;24:93–97.
  • Elsner L. A note on generalized Hessenberg matrices. Linear Algebra Appl. 2005;409:147–152.
  • Fiedler M, Vavrín Z. Generalized Hessenberg matrices. Linear Algebra Appl. 2004;380:95–105.
  • Abderramán Marrero J, Rachidi M. Companion factorization in the general group GL (n; ℂ) and applications. Linear Algebra Appl. 2011;434:1261–1271.
  • Eidelman Y, Gohberg I. On a new class of structured matrices. Integr. Equat. Oper. Th. 1999;34:293–324.
  • Abderramán Marrero J, Tomeo V. On the closed representation for the inverses of Hessenberg matrices. J. Comp. App. Math. 2012;236:2962–2970.
  • Abderramán Marrero J, Rachidi M, Tomeo V. On new algorithms for inverting Hessenberg matrices. J. Comp. App. Math. 2013;252:12–20.
  • Golub GH, Van Loan CF. Matrix computations. 3rd ed. Baltimore (MD): Johns Hopkins University Press; 1996.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.