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Jacobi method and Gauss-Seidel method ,

  1. Dec 3, 2012 #1
    1. The problem statement, all variables and given/known data

    for part c , it asked for showing both 2 method converge for any initial condition.
    I think we can show that by using $$ρ(T_{j}), ρ(T_{g}) <1 $$
    I want to know whether it's correct or not , and is there any faster method?
    2. Relevant equations
    $$ρ(A)$$ means spectral radius of matrix A.
    And $$ρ(T_{j})=D^{-1}(L+U) , ρ(T_{g})=(D+L)^{-1}U $$
    where$$ A=D-L-U$$ , D is the diagonal matrix -L is strictly lower-triangular part of A,
    -U is strictly upper-triangular part of A.

    3. The attempt at a solution
     

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  3. Dec 4, 2012 #2
    anyone can help ._. ?
     
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