Total least squares problems on infinite dimensional spaces. (15th March 2021)

• Record Type: Journal Article
• Authors: Contino, Maximiliano; Fongi, Guillermina; Maestripieri, Alejandra; Muro, Santiago
• Is Part Of: Inverse problems. Volume 37:Number 4(2021)
• Publication Date: 2021-03-15
• Subjects: total least squares problems -- Tikhonov regularization -- inverse problems; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abe3dd
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We study weighted total least squares problems on infinite dimensional spaces. We present some necessary and sufficient conditions for the regularized problem to have a solution. The existence of solution can also be assured for the regularized minimization problem with a constraint to special subsets. Furthermore, we show that a regularization in infinite dimensional total least squares problems is necessary, since in most cases the problem without regularization does not admit a solution.