GMBACK: A generalised minimum backward error algorithm for nonsymmetric linear systems A drawback of employing the residual error norm as a stopping condition in an iterative process is that the error must be small if the approximation is accurate. However, the converse need not be true. The main aims of this paper are to consider an alternative criterion for judging whether a given approximation is acceptable and to present an algorithm which computes an approximate solution to the linear system $Ax = b$ such that the normwise backward error meets some optimality condition.

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

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  1. Yang, Zhanshan; Zheng, Bing: Block minimum perturbation algorithm based on block Arnoldi process for nonsymmetric linear systems with multiple right-hand sides (2019)
  2. Hallman, Eric; Gu, Ming: LSMB: minimizing the backward error for least-squares problems (2018)
  3. Simoncini, Valeria; Szyld, Daniel B.: Recent computational developments in Krylov subspace methods for linear systems. (2007)
  4. Catinas, Emil: The inexact, inexact perturbed, and quasi-Newton methods are equivalent models (2005)
  5. Cǎtinaş, E.: Inexact perturbed Newton methods and applications to a class of Krylov solvers (2001)
  6. van Rienen, Ursula: Numerical methods in computational electrodynamics. Linear systems in practical applications (2001)
  7. Liu, Xiaoming; Lu, Zhiming; Liu, Yulu: Krylov subspace projection method and its application to oil reservoir simulation (2000)
  8. Cătinaş, Emil: On the high convergence orders of the Newton-GMBACK methods (1999)
  9. Meister, Andreas: Comparison of different Krylov subspace methods embedded in an implicit finite volume scheme for the computation of viscous and inviscid flow fields on unstructured grids (1998)
  10. Alléon, Guillaume; Benzi, Michele; Giraud, Luc: Sparse approximate inverse preconditioning for dense linear systems arising in computational electromagnetics (1997)
  11. Kasenally, Ebrahim M.; Simoncini, Valeria: Analysis of a minimum perturbation algorithm for nonsymmetric linear systems (1997)
  12. Kasenally, Ebrahim M.: GMBACK: A generalised minimum backward error algorithm for nonsymmetric linear systems (1995)