## Analysis of the SOR Iteration for the 9-point Laplacian, Volume 178212National Aeronautics and Space Administration, Langley Research Center, 1986 - Numerical analysis |

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9-POINT LAPLACIAN 9-pt line 9-pt point methods 9-pt point Ordering 9-pt stencil Adams and Jordan[1986 asymptotic change of variables complex conjugate consistently ordered matrices converge slightly faster convergence rate cos^h cosnh data flow determine the optimal eigen eigenmodes eigenvalue eigenvalue-eigenvector pairs eigenvector corresponding eigenvectors in variable equivalence classes Figure 3.6b five-point model problem four-color orderings Fourier analysis Garabedian's results given in Figure gives grid is colored grid points hence iteration matrix Jacobi method Laplace's equation line SOR methods lowest frequency multicolor orderings natural rowwise ordering nine-point stencil nodes Numerical optimal omega ordering R/B/G/O overrelaxation parallel computers Partial Differential Equations Point and Line point SOR methods pseudo SOR method quartic equation rate of convergence RB order real root Red/Black ordering Rowwise or Red/Black Section separation of variables SIAM Journal small h smooth initial data solving the quartic spectral radius spurious eigenvectors Stencil in Variable true SOR methods update formula values