Input: $A\mathrm{,}B$ , $w^{\left(0\right)}={\left[z_1^{\left(0\right)}\mathrm{,}{z}_2^{\left(0\right)}\mathrm{,}{\alpha }^{\left(0\right)}\mathrm{,}{\beta }^{\left(0\right)}\right]}^{\text{T}}\mathrm{,}{k}_{max}$ .

for $k=0,1,2,\cdots$ , until convergence

Choose ${\tau }^{\left(k\right)}$ .

Solve $M^{\left(k\right)}{u}^{\left(k\right)}=B_1{w}^{\left(k\right)}$ inexactly,

$\Vert {\mathcal{P}}^{-1}{M}^{\left(k\right)}{u}^{\left(k\right)}-{\mathcal{P}}^{-1}{B}_1{w}^{\left(k\right)}\Vert \le {\tau }^{\left(k\right)}\mathrm{.}$

end for

Output: $u^{\left(k_{max}\right)}$ .