East Asian J. Appl. Math., 10 (2020), pp. 381-398.
Published online: 2020-04
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HSS-based iteration methods for large systems of tensor equations $\mathcal{T}$($x$) = $b$ and $Ax$ = $\mathcal{T}$($x$) + $b$ are considered and conditions of their local convergence are presented. Numerical experiments show that for the equations $\mathcal{T}$($x$) = $b$, the Newton-HSS method outperforms the Newton-GMRES method. For nonlinear convection-diffusion equations the methods based on HSS iterations are generally more efficient and robust than the Newton-GMRES method.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.140819.071019}, url = {http://global-sci.org/intro/article_detail/eajam/16132.html} }HSS-based iteration methods for large systems of tensor equations $\mathcal{T}$($x$) = $b$ and $Ax$ = $\mathcal{T}$($x$) + $b$ are considered and conditions of their local convergence are presented. Numerical experiments show that for the equations $\mathcal{T}$($x$) = $b$, the Newton-HSS method outperforms the Newton-GMRES method. For nonlinear convection-diffusion equations the methods based on HSS iterations are generally more efficient and robust than the Newton-GMRES method.