A global solution for the structured total least squares problem with block circulant matrices
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 Nunstructured total least squares (TLS) problems. Th...
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| Veröffentlicht in: | SIAM journal on matrix analysis and applications 2005-01, Vol.27 (1), p.238-255 |
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| creator | BECK, Amir BEN-TAL, Aharon |
| description | 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 Nunstructured 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. |
| doi_str_mv | 10.1137/040612233 |
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We show that by applying the discrete Fourier transform (DFT), the STLS problem decomposes into Nunstructured 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.</abstract><cop>Philadelphia, PA</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/040612233</doi><tpages>18</tpages></addata></record> |
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| subjects | Algorithms Decomposition Exact sciences and technology Fourier analysis Fourier transforms Linear equations Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Sciences and techniques of general use Signal processing |
| title | A global solution for the structured total least squares problem with block circulant matrices |
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