136
Views
23
CrossRef citations to date
0
Altmetric
Miscellany

Solving EP singular linear systems

&
Pages 1395-1405 | Received 25 Feb 2004, Published online: 25 Jan 2007

References

References

  • Schwerdtfeger H (1950) Introduction to Linear Algebra, and the Theory of Matrices Noordhoff, P., Groningen.
  • Campbell SL Meyer CD (1979) Generalized Inverses of Linear Transformations Pitman, London
  • Shtykel , TL . (1995) . To the theory of degenerate systems of ordinary differential equations . Siberian Math. J. , 36 ( 5 ) : 1037 – 1049 .
  • Chen , YL . (1993) . A Cramer rule for solution of the general restricted linear equation . Linear Multilinear Algebra , 34 : 177 – 186 .
  • Ipsen , ICF and Meyer , CD . (1998) . The idea behind Krylov methods . Am. Math. Mon. , 105 : 889 – 899 .
  • Calvetti , D , Lewis , B and Reichel , L . (2000) . GMRES-type methods for inconsistent systems . Linear Algebra Appl. , 316 : 157 – 169 .
  • Zhang , SL , Oyanagi , Y and gihara , M . (2000) . Necessary and sufficient conditions for the convergence of orthomin(k) on singular and inconsistent linear systems . Numer. Math. , 87 : 391 – 405 .
  • Brown , PN and Walker , HF . (1997) . GMRES on (nearly) singular systems . SIAM J. Matrix Anal. Appl. , 18 ( 1 ) : 37 – 51 .
  • Wei , YM and Zhang , NM . (2003) . Condition number related with generalized inverse and constrained linear systems . J. Comput. Appl. Math. , 157 : 57 – 72 .
  • Zhang , NM and Wei , YM . (2003) . Perturbation bounds for the generalized inverse with application to constrained linear systems . Appl. Math. Comput. , 142 : 63 – 78 .
  • Elman , HC . (1999) . Preconditioning for the steady-state Navier-Stokes equations with low viscosity . SIAM J. Sci. Comput. , 20 ( 4 ) : 1299 – 1316 .
  • Harlowm , FH and Welch , JE . (1965) . Numerical calculation of times-dependent viscous incompressible flow of fluid with free surface . Phys. Fluids , 8 : 2182 – 2189 .
  • Saad , Y and Schultz , MH . (1986) . GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems . SIAM J. Sci. Stat. Comput. , 7 ( 3 ) : 858 – 869 .
  • Keller , C , Gould , NIM and Wathen , AJ . (2000) . Constraint preconditioning for indefinite linear systems . SIAM J. Matrix Anal. Appl. , 21 : 1300 – 1317 .

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.