Tensor Arnoldi-Tikhonov and GMRES-type methods for ill-posed problems with a t-product structure

DOI10.1007/s10915-021-01719-1zbMath1481.65060arXiv2110.04796OpenAlexW3207318799MaRDI QIDQ2063214

Ugochukwu O. Ugwu, Lothar Reichel

Publication date: 10 January 2022

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.04796

zbMATH Keywords

discrepancy principlelinear discrete ill-posed problemtensor Arnoldi processtensor Tikhonov regularizationt-product

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Iterative numerical methods for linear systems (65F10) Multilinear algebra, tensor calculus (15A69)

Related Items (7)

Weighted tensor Golub-Kahan-Tikhonov-type methods applied to image processing using a t-product ⋮ Spectral computation with third-order tensors using the t-product ⋮ The global Golub-Kahan method and Gauss quadrature for tensor function approximation ⋮ The Fréchet derivative of the tensor t-function ⋮ Numerical considerations of block GMRES methods when applied to linear discrete ill-posed problems ⋮ The new Krylov subspace methods for solving tensor equations via \(T\)-product ⋮ Unnamed Item

Uses Software

• Regularization tools
• tproduct

Cites Work

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• Tensor Decompositions and Applications
• Arnoldi methods for image deblurring with anti-reflective boundary conditions
• Factorization strategies for third-order tensors
• A tensor-based dictionary learning approach to tomographic image reconstruction
• Tensor-tensor products with invertible linear transforms
• Golub-Kahan bidiagonalization for ill-conditioned tensor equations with applications
• A new zero-finder for Tikhonov regularization
• Arnoldi-Tikhonov regularization methods
• Tikhonov regularization of large linear problems
• Tikhonov regularization and the L-curve for large discrete ill-posed problems
• On the regularizing properties of the GMRES method
• Krylov-type methods for tensor computations.I
• Old and new parameter choice rules for discrete ill-posed problems
• Generalized singular value decomposition with iterated Tikhonov regularization
• Generalized tensor function via the tensor singular value decomposition based on the T-product
• Iterative Tikhonov regularization of tensor equations based on the Arnoldi process and some of its generalizations
• A simplified L-curve method as error estimator
• On Krylov projection methods and Tikhonov regularization
• On the choice of subspace for large-scale Tikhonov regularization problems in general form
• Convergence analysis of minimization-based noise level-free parameter choice rules for linear ill-posed problems
• Regularization tools version \(4.0\) for matlab \(7.3\)
• T-Jordan canonical form and T-Drazin inverse based on the T-product
• GCV for Tikhonov regularization via global Golub–Kahan decomposition
• Facial Recognition Using Tensor-Tensor Decompositions
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
• Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
• An Order-$p$ Tensor Factorization with Applications in Imaging
• The tensor Golub–Kahan–Tikhonov method applied to the solution of ill‐posed problems with a t‐product structure
• Augmented GMRES-type versus CGNE methods for the solution of linear ill-posed problems
• Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging

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