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GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems

Jul 14, 2006
14 pages
Published in:
  • SIAM J.Sci.Statist.Comput. 7 (2006) 3, 856-869
  • Published: Jul 14, 2006
DOI:
reference search75 citations

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Abstract: (Society for Industrial and Applied Mathematics)
We present an iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an l2l_2 -orthogonal basis of Krylov subspaces. It can be considered as a generalization of Paige and Saunders’ MINRES algorithm and is theoretically equivalent to the Generalized Conjugate Residual (GCR) method and to ORTHODIR. The new algorithm presents several advantages over GCR and ORTHODIR.
  • nonsymmetric systems
  • Krylor subspaces
  • conjugate gradient
  • descent methods
  • minimal residual methods
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