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.