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\section{A Krylov two-stage algorithm}
+We propose a two-stage algorithm to solve large sparse linear systems of the form $Ax=b$ based on iterative Krylov sub-space methods.
\begin{algorithm}[!h]
\caption{A Krylov two-stage algorithm}
\begin{algorithmic}[1]
-\Input $A$ (sparse matrix), $b$ (right-hand side)
-\Output $x$ (solution vector)\vspace{0.2cm}
-\State Set the initial guess $x^0$
-\For {$k=1,2,3,\ldots$ until convergence}
-\State Solve iteratively $Ax^k=b$
-\State Add vector $x^k$ to Krylov basis $S$
-\If {$k$ mod $s=0$ {\bf and} not convergence}
-\State Compute dense matrix $R=AS$
-\State Solve least-squares problem $\|b-R\alpha\|_2$
-\State Compute minimizer $x^k=S\alpha$
-\State Reinitialize Krylov basis $S$
-\EndIf
-\EndFor
+ \Input $A$ (sparse matrix), $b$ (right-hand side)
+ \Output $x$ (solution vector)\vspace{0.2cm}
+ \State Set the initial guess $x^0$
+ \For {$k=1,2,3,\ldots$ until convergence}
+ \State Solve iteratively $Ax^k=b$
+ \State Add vector $x^k$ to Krylov basis $S$
+ \If {$k$ mod $s=0$ {\bf and} not convergence}
+ \State Compute dense matrix $R=AS$
+ \State Solve least-squares problem $\|b-R\alpha\|_2$
+ \State Compute minimizer $x^k=S\alpha$
+ \State Reinitialize Krylov basis $S$
+ \EndIf
+ \EndFor
\end{algorithmic}
\label{algo:01}
\end{algorithm}
