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
The Tensor Generalized Krylov Subspace Method with t-Product Structure for Solving Linear Discrete Ill-Posed Problems
DOI: 10.12677/AAM.2024.131024, PDF,    科研立项经费支持
作者: 王仕伟：成都理工大学数理学院，四川 成都
关键词: 离散不适定问题；广义Krylov子空间；t-积；正则化；Discrete Ill-Posed Problems； Generalized Krylov Subspaces； t-Product； Regularization
摘要: 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。
Abstract: 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.
文章引用：王仕伟. 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[J]. 应用数学进展, 2024, 13(1): 208-216. https://doi.org/10.12677/AAM.2024.131024

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