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 - <p style="text-align: justify;">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.</p>