Condition numbers of multidimensional mixed least squares-total least squares problems. (English) Zbl 1497.65070
Summary: This paper considers the multidimensional mixed least squares-total least squares (MTLS) problem which arises in the regression model, signal processing and the problem of space coordinate transformation. Firstly, the MTLS problem is proved to be equivalent to a weighted total least squares problem in the limit sense. Then, the perturbation analysis and explicit normwise, mixed and componentwise condition number formulae for the MTLS problem are presented. Tight and computable upper bounds for these condition numbers are also given. The results include the ones for the single-right-hand-side MTLS as special cases. Finally in the numerical experiments, the tightness of condition numbers and upper bounds in evaluating the forward errors is also shown.
MSC:
| 65F20 | Numerical solutions to overdetermined systems, pseudoinverses |
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
Keywords:
multidimensional mixed least squares-total least squares problem; weighted TLS problem; condition numberSoftware:
VanHuffelReferences:
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