Abstract
We study the structured total least squares (STLS) problem of system of linear equations Ax = b, where A has a block circulant structure with N blocks. We show that by applying the discrete Fourier transform (DFT), the STLS problem decomposes into N unstructured total least squares (TLS) problems. The N solutions of these problems are then assembled to generate the optimal global solution of the STLS problem. Similar results are obtained for elementary block circulant matrices. Here the optimal solution is obtained by assembling two solutions: one of an unstructured TLS problem and the second of a multidimensional TLS problem.
| Original language | English |
|---|---|
| Pages (from-to) | 238-255 |
| Number of pages | 18 |
| Journal | SIAM Journal on Matrix Analysis and Applications |
| Volume | 27 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2006 |
| Externally published | Yes |
Keywords
- Block circulant matrices
- Discrete fourier transform
- Structured total least squares