Filter factors of truncated tls regularization with multiple observations
| dc.contributor.author | Plešinger Martin | cs |
| dc.contributor.author | Žáková Jana | cs |
| dc.contributor.author | Hnětynková Iveta | cs |
| dc.date.accessioned | 2018-09-25T12:15:50Z | |
| dc.date.available | 2018-09-25T12:15:50Z | |
| dc.date.issued | 2017 | cs |
| dc.description.abstract | The total least squares (TLS) and truncated TLS (T-TLS) methods are widely known linear data fitting approaches, often used also in the context of very ill-conditioned, rank-deficient, or ill-posed problems. Regularization properties of T-TLS applied to linear approximation problems $Ax\approx b$ were analyzed by Fierro, Golub, Hansen, and O'Leary (1997) through the so-called filter factors allowing to represent the solution in terms of a filtered pseudoinverse of $A$ applied to $b$. This paper focuses on the situation when multiple observations $b_1,\ldots,b_d$ are available, i.e., the T-TLS method is applied to the problem $AX\approx B$, where $B=[b_1,\ldots,b_d]$ is a matrix. It is proved that the filtering representation of the T-TLS solution can be generalized to this case. The corresponding filter factors are explicitly derived. | |
| dc.format.extent | 16 | cs |
| dc.identifier.doi | 10.21136/AM.2017.0228-16 | |
| dc.identifier.issn | 0862-7940 | cs |
| dc.identifier.uri | https://dspace.tul.cz/handle/15240/31445 | |
| dc.identifier.uri | https://articles.math.cas.cz/10.21136/AM.2017.0228-16 | |
| dc.language.iso | eng | cs |
| dc.publisher | Springer | cs |
| dc.relation.ispartofseries | 0 | cs |
| dc.relation.uri | https://link.springer.com/article/10.21136/AM.2017.0228-16 | cs |
| dc.subject | truncated total least squares | cs |
| dc.subject | multiple right-hand sides | cs |
| dc.subject | eigenvalues of rank-d update | cs |
| dc.subject | ill-posed problem | cs |
| dc.subject | regularization | cs |
| dc.subject | filter factors | cs |
| dc.title | Filter factors of truncated tls regularization with multiple observations | en |
| local.citation.epage | 105-120 | cs |
| local.citation.spage | 105-120 | cs |
| local.identifier.publikace | 4908 | |
| local.identifier.wok | 400889400002 | en |
| local.relation.issue | 2 | cs |
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