# Jacobi method and Gauss-Seidel method ,

1. Dec 3, 2012

### sigh1342

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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2. Dec 4, 2012

### sigh1342

anyone can help ._. ?