%0 Journal Article
%T 求解大规模线性问题的张量GMRES算法<br>Tensor GMRES Algorithm for Solving Large-Scale Linear Problems
%A 王仕伟
%A 杨志
%A 冷震北
%J Advances in Applied Mathematics
%P 1007-1018
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.144223
%X 彩色图像和视频通常可以被描述为高阶张量。本文基于三阶张量t-积&#65292;讨论了Krylov子空间方法用以解决图像恢复中的大规模线性问题。本文通过张量GMRES算法构建Krylov子空间&#65292;将大规模线性问题转换为小规模问题&#65292;且构建的子空间始终保持张量的空间结构。数值例子和彩色图像修复的应用说明了算法的有效性。<br>Color images and video sequences can typically be characterized as higher-order tensors. This paper investigates Krylov subspace methods based on the third-order tensor t-product for solving large-scale linear systems arising in image restoration. This paper employs the tensor GMRES algorithm to construct the Krylov subspace, effectively reducing large-scale linear problems to manageable small-scale formulations, while consistently preserving the spatial architecture of tensors within the constructed subspace. Numerical experiments and applications in color image inpainting demonstrate the efficacy of the proposed methodology.
%K 大规模线性问题&#65292
%K Krylov子空间方法&#65292
%K t-积&#65292
%K GMRES<br>Large-Scale Linear Problems
%K Krylov Subspace Methods
%K t-Product
%K GMRES
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=113397