DQGMRES: a direct quasi-minimal residual algorithm based on incomplete orthogonalization. A truncated version of the GMRES method for solving large sparse systems of linear algebraic equations is presented. The authors propose the DQGMRES algorithm, which is based on the incomplete Arnoldi orthogonalization process and computes a sequence of approximate solutions with the quasi-minimal residual property. The new algorithm is studied theoretically and tested extensively on a number of numerical examples.

References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Wang, Liping; Zhu, Yan: Hybrid methods based on LCG and GMRES (2016)
  2. Novati, Paolo; Russo, Maria Rosaria: A GCV based Arnoldi-Tikhonov regularization method (2014)
  3. Buttari, Alfredo; Dongarra, Jack; Kurzak, Jakub; Luszczek, Piotr; Tomov, Stanimire: Using mixed precision for sparse matrix computations to enhance the performance while achieving 64-bit accuracy. (2008)
  4. Simoncini, Valeria; Szyld, Daniel B.: Recent computational developments in Krylov subspace methods for linear systems. (2007)
  5. Simoncini, Valeria; Szyld, Daniel B.: The effect of non-optimal bases on the convergence of Krylov subspace methods (2005)
  6. Saad, Yousef: Iterative methods for sparse linear systems. (2003)
  7. Zavorin, Ilya; O’Leary, Dianne P.; Elman, Howard: Complete stagnation of GMRES (2003)
  8. Dayar, Tuugrul; Stewart, William J.: Comparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chains (2000)
  9. Chan, T.F.; Chow, E.; Saad, Y.; Yeung, M.C.: Preserving symmetry in preconditioned Krylov subspace methods (1999)
  10. Jia, Zhongxiao: On IGMRES: An incomplete generalized minimal residual method for large unsymmetric linear systems (1998)
  11. Saad, Y.; Wu, K.: DQGMRES: a direct quasi-minimal residual algorithm based on incomplete orthogonalization (1996)
  12. Bruaset, Are Magnus: A survey of preconditioned iterative methods (1995)
  13. Saad, Yousef; Wu, Kesheng: Design of an iterative solution module for a parallel sparse matrix library (P_SPARSLIB) (1995)