Solution
= Solution
The full, undamped <Newton's method in optimization> step is
$$
x_1=x_0-H_f(x_0)^{-1}\nabla f(x_0)
=x_0-(2A)^{-1}(2Ax_0+b)
=-\tfrac12A^{-1}b.
$$
The <eigenvector> identity gives $A^{-1}b=2b$. Consequently \b[$x_1=-b$ for every starting point]. This is a <one-step Newton solution of a quadratic stationary equation>: its <gradient> is an <affine function>, so a single exact Newton solve resolves it completely.