howpublished = {\url{http://www.mcs.anl.gov/petsc}},
year = {2014}
}
+
+
+@misc{Dav97,
+ author = {Davis, T. and Hu, Y.},
+ title = {The {U}niversity of {F}lorida Sparse Matrix Collection},
+ year = {1997},
+ note = {Digest, \url{http://www.cise.ufl.edu/research/sparse/matrices/}},
+ }
\ No newline at end of file
\State Set the initial guess $x_0$
\For {$k=1,2,3,\ldots$ until convergence (error$<\epsilon_{tsirm}$)} \label{algo:conv}
\State $[x_k,error]=Solve(A,b,x_{k-1},max\_iter_{kryl})$ \label{algo:solve}
- \State $S_{k \mod s}=x_k$ \label{algo:store}
+ \State $S_{k \mod s}=x_k$ \label{algo:store} \Comment{update column (k mod s) of S}
\If {$k \mod s=0$ {\bf and} error$>\epsilon_{kryl}$}
\State $R=AS$ \Comment{compute dense matrix} \label{algo:matrix_mul}
\State $\alpha=Least\_Squares(R,b,max\_iter_{ls})$ \label{algo:}
In order to see the influence of our algorithm with only one processor, we first
-show a comparison with the standard version of GMRES and our algorithm. In
-Table~\ref{tab:01}, we show the matrices we have used and some of them
-characteristics. For all the matrices, the name, the field, the number of rows
-and the number of nonzero elements are given.
+show a comparison with GMRES or FGMRES and our algorithm. In Table~\ref{tab:01},
+we show the matrices we have used and some of them characteristics. Those
+matrices are chosen from the Davis collection of the University of
+Florida~\cite{Dav97}. They are matrices arising in real-world applications. For
+all the matrices, the name, the field, the number of rows and the number of
+nonzero elements are given.
\begin{table}[htbp]
\begin{center}
