244
Views
8
CrossRef citations to date
0
Altmetric
Articles

On least squares solutions subject to a rank restriction

Pages 264-273 | Received 16 Dec 2012, Accepted 29 Sep 2013, Published online: 23 Jan 2014

References

  • Ben-Israel A, Greville TNE. Generalized inverses: theory and applications. 2nd ed. Berlin: Springer; 2003.
  • Eckart C, Young G. The approximation of one matrix by another of lower rank. Psychometrika. 1936;1:211–218.
  • Mirsky L. Symmetric gauge functions and unitarily invariant norms. Quart. J. Math. 1960;11:50–59.
  • Duan G-R. Analysis and design of descriptor linear systems. New York: Springer; 2010.
  • Friedland S, Torokhti A. Generalized rank-constrained matrix approximations. SIAM J. Matrix Anal. Appl. 2007;29:656–659.
  • Wei M, Wang Q. On rank-constrained Hermitian nonnegative-definite least squares solutions to the matrix equation AX AH = B. Int. J. Comput. Math. 2007;84:945–952.
  • Wei M, Shen D. Minimum rank solutions to the matrix approximation problems in the spectral norm. SIAM J. Matrix Anal. Appl. 2012;33:940–957.
  • Golub GH, Hoffman A, Stewart GW. A generalization of the Eckart–Young–Mirsky matrix approximation theorem. Linear Algebra Appl. 1987;88–89:317–327.
  • Demmel JW. The smallest perturbation of a submatrix which lowers the rank and constrained total least squares problems. SIAM J. Numer. Anal. 1987;24:199–206.
  • Guttman L. Enlargement methods for computing the inverse matrix. Ann. Math. Statist. 1946;17:336–343.
  • Marsaglia G, Styan GPH. Equalities and inequalities for ranks of matrices. Linear Multilinear Algebra. 1974;2:269–292.
  • Meyer CD Jr. Generalized inverses and ranks of block matrices. SIAM J. Appl. Math. 1973;25:597–602.
  • Golub GH, Van Loan CF. Matrix computations. 2nd ed. Baltimore, MD: The Johns Hopkins University Press; 1989.
  • Wei M. Perturbation theory for the Eckart-Young-Mirsky theorem and the constrained total least squares problem. Linear Algebra Appl. 1998;280:267–287.

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.