English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper is concerned with solving ill-posed tensor linear equations. Thesekinds of equations may appear from finite difference discretization ofhigh-dimensional convection-diffusion problems or when partial differentialequations in many dimensions are discretized by collocation spectral methods.Here, we propose the Tensor Golub--Kahan bidiagonalization (TGKB) algorithm inconjunction with the well known Tikhonov regularization method to solve thementioned problems. Theoretical results are presented to discuss onconditioning of the Stein tensor equation and to reveal that how the TGKBprocess can be exploited for general tensor equations. In the last section,some classical test problems are examined to numerically illustrate thefeasibility of proposed algorithms and also applications for color imagerestoration are considered.

On the Golub--Kahan bidiagonalization for ill-posed tensor equations with applications to color image restoration