Steepest descent method

We denote the initial guess for \( \hat{x} \) as \( \hat{x}_0 \). We can assume without loss of generality that

$$ \begin{equation*} \hat{x}_0=0, \end{equation*} $$

or consider the system

$$ \begin{equation*} \hat{A}\hat{z} = \hat{b}-\hat{A}\hat{x}_0, \end{equation*} $$

instead.