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Foil 38 Over Relaxation (SOR) and Relation to Jacobi and Gauss-Seidel

From Fox Presentation Fall 1995 CPS615 Basic Simulation Track for Computational Science -- Fall Semester 95. by Geoffrey C. Fox
1 Jacobi and Gauss Seidel give a formula for x(k+1) in terms of x(k) call this x(k+1)
2 Overrelaxation forms x(k+1) = w x(k+1) + (1-w)x(k)
3 Typically only 0 < w < 2 is sensible w < 1 is relaxation 1 < w < 2 is over relaxation
4 First consider relaxation for Jacobi x(k+1) = wx(k+1) + (1-w)x(k)
5 There is an iteration matrix
  • G=M-1 N which on diagonalization we called K
  • with G=PTKP and P an orthogonal matrix
in Table To:

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