CGLS Algorithm:

Initialinize: m = 0, u(0) = f(k), r(0) = y − Pu(0), s(0) = PTr(0). Do the Steps 1–5 for M times.

$a^{(m)}={\Vert P^T{r}^{(m)}\Vert }_2^2/{\Vert P{s}^{(m)}\Vert }_2^2$ u(m+1) = u(m) + a(m)s(m) r(m+1) = r(m) − a(m)Ps(m) $b^{(m)}={\Vert P^T{r}^{(m+1)}\Vert }_2^2/{\Vert P^T{r}^{(m)}\Vert }_2^2$ s(m+1) = PTr(m+1) + b(m)s(m) v(k+1) = u(M)