Name
Title | ||
|---|---|---|
Tensor Arnoldi-Tikhonov and GMRES-Type Methods for Ill-Posed Problems with a t-Product Structure |
Abstract | ||
|---|---|---|
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 t-product Arnoldi (t-Arnoldi) process is defined and applied to reduce a large-scale Tikhonov regularization problem for third order tensors to a problem of small size. The data may be represented by a laterally oriented matrix or a third order tensor, and the regularization operator is a third order tensor. The discrepancy principle is used to determine the regularization parameter and the number of steps of the t-Arnoldi process. Numerical examples compare results for several solution methods, and illustrate the potential superiority of solution methods that tensorize over solution methods that matricize linear discrete ill-posed problems for third order tensors. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1007/s10915-021-01719-1 | JOURNAL OF SCIENTIFIC COMPUTING |
Keywords | DocType | Volume |
Discrepancy principle, Linear discrete ill-posed problem, Tensor Arnoldi process, T-product, Tensor Tikhonov regularization | Journal | 90 |
Issue | ISSN | Citations |
1 | 0885-7474 | 1 |
PageRank | References | Authors |
0.36 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lothar Reichel | 1 | 453 | 95.02 |
| Ugochukwu O. Ugwu | 2 | 1 | 0.36 |