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Machine learningKrylov Subspace Iterative

GMRES

GMRES (Generalized Minimal Residual) er en iterativ metode til løsning af store sparsomme usymmetriske eller ikke-symmetriske lineære systemer Ax = b, udviklet af Saad og Schultz i 1986. Den opbygger en ortonormal Krylov-basis ved hjælp af Arnolds metode og løser et mindste-kvadraters problem for at minimere residualet ved hver iteration.

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Kilder

  1. Saad, Y., & Schultz, M. H. (1986). GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing, 7(3), 856–869. DOI: 10.1137/0907058
  2. Walker, H. F. (1988). Implementation of the GMRES method using Householder reflections. SIAM Journal on Scientific and Statistical Computing, 9(1), 152–163. DOI: 10.1137/0909010
  3. Saad, Y. (2003). Iterative Methods for Sparse Linear Systems (2nd ed.). SIAM. DOI: 10.1137/1.9780898718003

Sådan citerer du denne side

ScholarGate. (2026, June 3). Generalized Minimal Residual Method. ScholarGate. https://scholargate.app/da/numerical-methods/gmres

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ScholarGateGMRES (Generalized Minimal Residual Method). Hentet 2026-06-15 fra https://scholargate.app/da/numerical-methods/gmres · Datasæt: https://doi.org/10.5281/zenodo.20539026