In a recent work by the author [Linear Algebra Appl. 298 (1999) 99] Krylov subspace methods were derived for Drazin-inverse solution of consistent or inconsistent linear systems of the form Ax=b, where A € C^(NxN) is a singular and in general non-hermitian matrix that has arbitrary index. One of these methods, modeled after the Generalized Conjugate Residual method (GCR) and denoted DGCR, is considered in the present work again. It is shown that all of the approximations produced by DGCR exist, and a GMRES like algorithm, denoted DGMRES, for its implementation is derived. Like GMRES, DGMRES too is economical computationally and storagewise.

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Safarzadeh, Malihe; Salemi, Abbas: DGMRES and index numerical range of matrices (2018)
  2. Aminikhah, Hossein; Jamalian, Ali: A new algorithm for computing eigenpairs of matrices (2011)
  3. Hayami, Ken; Sugihara, Masaaki: A geometric view of Krylov subspace methods on singular systems. (2011)
  4. Zhang, Naimin: A note on preconditioned GMRES for solving singular linear systems (2010)
  5. Taheri, S.H.; Ghazvini, H.; Saberi-Nadjafi, J.; Biazar, J.: A hybrid of the restarted Arnoldi and electromagnetism meta-heuristic methods for calculating eigenvalues and eigenvectors of a non-symmetric matrix (2007)
  6. Cui, Xiaoke; Diao, Huaian: Condition number for the $W$-weighted Drazin inverse and its applications in the solution of rectangular linear system (2006)
  7. Zhou, Jieyong; Wei, Yimin: A two-step algorithm for solving singular linear systems with index one (2006)
  8. Zhou, Jieyong; Wei, Yimin: The analysis of restart DGMRES for solving singular linear systems (2006)
  9. Wei, Yimin; Diao, Huaian: Condition number for the Drazin inverse and the Drazin-inverse solution of singular linear system with their condition numbers (2005)
  10. Zhou, Jieyong; Wei, Yimin: DFOM algorithm and error analysis for projection methods for solving singular linear system (2004)
  11. Zhou, Jieyong; Wei, Yiming: Perturbation analysis of singular linear systems with arbitrary index. (2003)
  12. Sidi, Avram: DGMRES: A GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems (2001)