%0 Journal Article
%T 含t-积结构的张量广义Krylov子空间方法求解线性离散不适定问题<br>The Tensor Generalized Krylov Subspace Method with t-Product Structure for Solving Linear Discrete Ill-Posed Problems
%A 王仕伟
%J Advances in Applied Mathematics
%P 208-216
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/AAM.2024.131024
%X 本文讨论了基于三阶张量的t-积形式，将广义Krylov子空间方法在解决大规模线性离散不适定问题中的应用。针对于离散不适定问题，首先确定正则化参数，并将一系列投影应用到广义的Krylov子空间上。数据张量是一般的三阶张量或由横向定向矩阵定义的张量。在数值例子和彩色图像修复中的应用说明了该方法的有效性。<br />
This article discusses the application of the generalized Krylov subspace method in solving large-scale linear discrete ill-posed problems based on the t-product form of third-order tensors. For discrete ill-posed problems, the regularization parameters are first determined, and a series of projections are applied to the generalized Krylov subspace. A data tensor is a general third-order tensor or a tensor defined by a transversely oriented matrix. The application of this method in nu-merical examples and color image restoration demonstrates its effectiveness.
%K 离散不适定问题，广义Krylov子空间，t-积，正则化<br>Discrete Ill-Posed Problems
%K Generalized Krylov Subspaces
%K t-Product
%K Regularization
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=79317