Tensor Arnoldi–Tikhonov and GMRES-Type Methods for Ill-Posed Problems with a t-Product Structure

This paper describes solution methods for linear discrete ill-posed problems defined by third order tensors and the t-product formalism introduced in (Linear Algebra Appl 435:641–658, 2011). A Arnoldi (t-Arnoldi) process is applied to reduce a large-scale Tikhonov regularization problem of small size. The data may be represented laterally oriented matrix or tensor, operator tensor. discrepancy principle used determine parameter number steps t-Arnoldi process. Numerical examples compare results several methods, illustrate potential superiority that tensorize over matricize tensors.