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The Convergence Of SOR iteration method

  1. Oct 12, 2013 #1
    1. The problem statement, all variables and given/known data
    show SOR iteration method converges for the system.
    $$6x+4y+2z=11$$
    $$4x+7y+4z=3$$
    $$2x+4y+5=-3$$


    2. Relevant equations

    if the coeff. matrix is positive definite matrix and 0≤ω≤2. Then SOR converge for any initial guess.
    Or if $$ρ(T_{ω})$$≥|ω-1|, then SOR converge for any initial guess.ρ(T) means the largest magnitude of all eigenvalue of T.$$T_{ω}=(I − ωL)^{-1} ((1 − ω)I + ωU)$$
    Or any norm of $$T_{ω} <1 $$ Then SOR converge for any initial guess

    3. The attempt at a solution
    I found that the coeff. matrix is not positive definite matrix . and the ρ(T) is hard to find .
    Any other method ? Or what I miss. Thanks you :blushing:
     
  2. jcsd
  3. Oct 12, 2013 #2

    fzero

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    Can you explain how you drew that conclusion? The coefficient matrix has positive eigenvalues.
     
  4. Oct 13, 2013 #3
    Oh I find that the value $$x^tAx$$ that I was computed is wrong . :frown:
    Thanks you so much :tongue:
     
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