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1 (20%) (Linear systems) Given a linear system C1 +33 2 One can convert it into an iterative formula x(n+1) TX(m) + c where

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Jacobi: X(K+1)=TX(N4 C where T--D1(LHU), C=D-1b, A=l+D+U a bc Gauss-Seidel. X(K+1)--(L+D)1Ux®) + (L+D)1 b = TX(k) + C a bc

1" (20%) (Linear systems) Given a linear system C1 +33 2 One can convert it into an iterative formula x(n+1) TX(m) + c where X(n) = (a (n),X(n), a (n))t įs the approximated solution at the nth iteration, T3x3 is the iterative matrix and caxi is the vector associated with the correspondent iterative method. (a) (5 %) Compute the associated matrix T and vector c associated with Jacobi method. (b) (5 %) Compute (T) and determine if Jacobi method converges. (c) (5 %) Compute the associated matrix T and vector c associated with Gauss-Seidel method. (d) (5 %) Compute ρ(T) and determine if Gauss-Seidel method con- verges.
Jacobi: X(K+1)=TX(N4 C where T--D1(LHU), C=D-1b, A=l+D+U a bc Gauss-Seidel. X(K+1)--(L+D)'1Ux®) + (L+D)'1 b = TX(k) + C a bc u-dx
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