  In this paper, we propose different algorithms for the solution of a tensor
linear discrete ill-posed problem arising in the application of the meshless
method for solving PDEs in three-dimensional space using multiquadric radial
basis functions. It is well known that the truncated singular value
decomposition (TSVD) is the most common effective solver for ill-conditioned
systems, but unfortunately the operation count for solving a linear system with
the TSVD is computationally expensive for large-scale matrices. In the present
work, we propose algorithms based on the use of the well known Einstein product
for two tensors to define the tensor global Arnoldi and the tensor Gloub Kahan
bidiagonalization algorithms. Using the so-called Tikhonov regularization
technique, we will be able to provide computable approximate regularized
solutions in a few iterations.
