Volume 10, Issue 2
On HSS-Based Iteration Methods for Two Classes of Tensor Equations

East Asian J. Appl. Math., 10 (2020), pp. 381-398.

Published online: 2020-04

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• Abstract

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.

15A69, 65F10, 65W05

dengmingyu@live. com (Ming-Yu Deng)

xpguo@math.ecnu.edu. cn (Xue-Ping Guo)

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@Article{EAJAM-10-381, author = {Deng , Ming-Yu and Guo , Xue-Ping}, title = {On HSS-Based Iteration Methods for Two Classes of Tensor Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {2}, pages = {381--398}, abstract = {

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} }
TY - JOUR T1 - On HSS-Based Iteration Methods for Two Classes of Tensor Equations AU - Deng , Ming-Yu AU - Guo , Xue-Ping JO - East Asian Journal on Applied Mathematics VL - 2 SP - 381 EP - 398 PY - 2020 DA - 2020/04 SN - 10 DO - http://doi.org/10.4208/eajam.140819.071019 UR - https://global-sci.org/intro/article_detail/eajam/16132.html KW - Tensor equation, HSS iteration, k-mode product, convergence, large sparse system. AB -

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.

Ming-YuDeng & Xue-PingGuo. (2020). On HSS-Based Iteration Methods for Two Classes of Tensor Equations. East Asian Journal on Applied Mathematics. 10 (2). 381-398. doi:10.4208/eajam.140819.071019
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