3 research outputs found
On the Golub--Kahan bidiagonalization for ill-posed tensor equations with applications to color image restoration
This paper is concerned with solving ill-posed tensor linear equations. These
kinds of equations may appear from finite difference discretization of
high-dimensional convection-diffusion problems or when partial differential
equations in many dimensions are discretized by collocation spectral methods.
Here, we propose the Tensor Golub--Kahan bidiagonalization (TGKB) algorithm in
conjunction with the well known Tikhonov regularization method to solve the
mentioned problems. Theoretical results are presented to discuss on
conditioning of the Stein tensor equation and to reveal that how the TGKB
process can be exploited for general tensor equations. In the last section,
some classical test problems are examined to numerically illustrate the
feasibility of proposed algorithms and also applications for color image
restoration are considered
Tensor extrapolation methods with applications
In this paper, we mainly develop the well-known vector and matrix polynomial
extrapolation methods in tensor framework. To this end, some new products
between tensors are defined and the concept of positive definitiveness is
extended for tensors corresponding to T-product. Furthermore, we discuss on the
solution of least-squares problem associated with a tensor equation using
Tensor Singular Value Decomposition (TSVD). Motivated by the effectiveness of
proposed vector extrapolation method in [Numer. Algorithms, 51 (2009),
195--208], we describe how an extrapolation technique can be also implemented
on the sequence of tensors produced by truncated TSVD (TTSVD) for solving
possibly ill-posed tensor equations.Comment: This is a research pape
On some tensor tubal-Krylov subspace methods via the T-product
In the present paper, we introduce new tensor Krylov subspace methods for
solving linear tensor equations. The proposed methods use the well known
T-product for tensors and tensor subspaces related to tube fibers. We introduce
some new tensor products and the related algebraic properties. These new
products will enable us to develop third-order the tensor tubal GMRES and the
tensor tubal Golub Kahan methods. We give some properties related to these
methods and proopse some numerical experiments.Comment: arXiv admin note: text overlap with arXiv:2006.0713