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

作　　者：王仕伟 

机构地区：[1]成都理工大学数理学院,四川 成都

出　　处：《应用数学进展》2024年第1期208-216,共9页Advances in Applied Mathematics

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。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.

关 键 词：离散不适定问题 广义Krylov子空间 t-积 正则化 

分 类 号：O15[理学—数学]