Solution
= Solution
The <gradient descent> iteration is
$$
\boxed{x^{(k+1)}=(I-\alpha A)x^{(k)}+\alpha b}.
$$
For the error $e^{(k)}=x^{(k)}-A^{-1}b$,
$$
e^{(k+1)}=(I-\alpha A)e^{(k)}.
$$
Part (a) shows that convergence for every initial vector is equivalent to
$|1-\alpha\lambda_i|<1$ for every eigenvalue of $A$. Since all eigenvalues are positive,
$$
\boxed{0<\alpha<\frac2{\lambda_{\max}(A)}}.
$$