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\subsection{Influence of parameters for TSIRM}\r
-In this section we present some experimental results in order to study the influence of some parameters on the TSIRM algorithm which are: the method to solve the linear least-squares problem in the minimization process, the number of inner iterations $max\_iter_{kryl}$, and the size $s$ of matrix $AS$ (i.e. matrix $S$) of the least-squares problem. We conducted experiments on $16$ cores to solve linear and nonlinear problems of size $200,000$ components per core. We solved problems token from examples {\it ksp} and {\it snes} of PETSc~\cite{ksp,snes}. We fixed some parameters of the TSIRM algorithm as follows: the nonlinear systems are solved with a precision of $10^{-8}$, the tolerance threshold and the maximum number of iterations of TSIRM algorithm are $\epsilon_{tsirm}=10^{-10}$ and $max\_iter_{tsirm}=10,000$, the FGMRES method is used as the inner solver with a tolerance threshold $\epsilon_{kryl}=10^{-10}$, the additive Schwarz method (ASM) is used as a preconditioner, and the least-squares problem is solved with a precision $\epsilon_{ls}=10^{-40}$ in the minimization process.\r
+In this section we present some experimental results in order to study the influence of some parameters on the TSIRM algorithm which are: the method to solve the linear least-squares problem in the minimization process, the number of inner iterations $max\_iter_{kryl}$, and the size $s$ of matrix $AS$ (i.e. matrix $S$) of the least-squares problem. We conducted experiments on $16$ cores to solve linear and nonlinear problems of size $200,000$ components per core. We solved problems token from examples {\it ksp}~\cite{ksp} and {\it snes}~\cite{snes} of PETSc. We fixed some parameters of the TSIRM algorithm as follows: the nonlinear systems are solved with a precision of $10^{-8}$, the tolerance threshold and the maximum number of iterations of TSIRM algorithm are $\epsilon_{tsirm}=10^{-10}$ and $max\_iter_{tsirm}=10,000$, the FGMRES method is used as the inner solver with a tolerance threshold $\epsilon_{kryl}=10^{-10}$, the additive Schwarz method (ASM) is used as a preconditioner, and the least-squares problem is solved with a precision $\epsilon_{ls}=10^{-40}$ in the minimization process.\r
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%time mpirun ../ex34 -da_grid_x 147 -da_grid_y 147 -da_grid_z 147 -ksp_type tsirm -ksp_pc_type asm -pc_type ksp -ksp_tsirm_tol 1e-10 -ksp_tsirm_maxiter 10000 -ksp_ksp_type fgmres -ksp_tsirm_max_inner_iter 30 -ksp_tsirm_inner_tol 1e-10 -ksp_tsirm_cgls 0 -ksp_tsirm_tol_ls 1.e-40 -ksp_tsirm_maxiter_ls 20 -ksp_tsirm_size_ls 10\r
\begin{figure}[htbp]\r
