Jacobi method and Gauss-Seidel method ,

[sigh1342]

Homework Statement

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?

Homework 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.

The Attempt at a Solution

 

[sigh1342]

anyone can help ._. ?