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.

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