= Landweber iteration with a Tikhonov initial value
{c}
{title2=$x_0=(A^*A+\alpha I)^{-1}A^*y,\qquad x_{n+1}=x_n+\alpha^{-1}A^*(y-Ax_n)$}
Initialize <Landweber iteration> by <Tikhonov regularization>, then use step $1/\alpha$. Writing $B=A^*A$ and $R=I-B/\alpha$, the iterate is $x_n=R^n(B+\alpha I)^{-1}A^*y+\alpha^{-1}\sum_{j=0}^{n-1}R^jA^*y$. For nonzero $A$, the sufficient convergence condition is $\alpha>\|A\|^2/2$. This explicit method differs from <Iterated Tikhonov regularization>, whose update is $(B+\alpha I)x_{n+1}=\alpha x_n+A^*y$.
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