Numerical Analysis · Linear Systems · 1 mark · Multiple choice
$A=\begin{pmatrix}2&-1&1\\1&2&-1\\-1&1&2\end{pmatrix}$. For (A+εI)x=b, ε>0, I: Jacobi converges for every start. II: Gauss–Seidel converges for every start. Choose truth values.
Each diagonal entry has magnitude 2+ε while the absolute off-diagonal row sum is 2. Strict row diagonal dominance guarantees convergence of both Jacobi and Gauss–Seidel for any initial approximation. **A**.
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