Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense
| Autor: | Martin Plešinger, Diana M. Sima, Iveta Hnětynková |
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| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
010102 general mathematics Structure (category theory) 010103 numerical & computational mathematics Sense (electronics) Approx 01 natural sciences Combinatorics Reduction (complexity) Core (graph theory) Linear approximation 0101 mathematics Invariant (mathematics) Total least squares Analysis Mathematics |
| Zdroj: | SIAM Journal on Matrix Analysis and Applications. 37:861-876 |
| ISSN: | 1095-7162 0895-4798 |
| Popis: | Recently it was shown how necessary and sufficient information for solving an orthogonally invariant linear approximation problem $AX\approx B$ with multiple right-hand sides can be revealed through the so-called core problem reduction; see [I. Hnětynkova, M. Plesinger, and Z. Strakos, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 917--931]. The total least squares (TLS) serves as an important example of such approximation problem. Solvability of TLS was discussed in the full generality in [I. Hnětynkova et al., SIAM J. Matrix Anal. Appl., 32 (2011), pp. 748--770]. This theoretical study investigates solvability of core problems with multiple right-hand sides in the TLS sense. It is shown that, contrary to the single right-hand side case, a core problem with multiple right-hand sides may not have a TLS solution. Further possible internal structure of core problems is studied. Outputs of the classical TLS algorithm for the original problem $AX\approx B$ and for the core problem within $AX\approx B$ are compared. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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