| Title:
|
Filter factors of truncated TLS regularization with multiple observations (English) |
| Author:
|
Hnětynková, Iveta |
| Author:
|
Plešinger, Martin |
| Author:
|
Žáková, Jana |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
62 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
105-120 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
truncated total least squares |
| Keyword:
|
multiple right-hand sides |
| Keyword:
|
eigenvalues of rank-$d$ update |
| Keyword:
|
ill-posed problem |
| Keyword:
|
regularization |
| Keyword:
|
filter factors |
| MSC:
|
15A18 |
| MSC:
|
65F20 |
| MSC:
|
65F22 |
| MSC:
|
65F25 |
| MSC:
|
65F30 |
| idZBL:
|
Zbl 06738484 |
| idMR:
|
MR3647038 |
| DOI:
|
10.21136/AM.2017.0228-16 |
| . |
| Date available:
|
2017-03-31T09:45:01Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146698 |
| . |
| Reference:
|
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