# On the condition number of the total least squares problem

@article{Jia2011OnTC, title={On the condition number of the total least squares problem}, author={Zhongxiao Jia and Bingyu Li}, journal={Numerische Mathematik}, year={2011}, volume={125}, pages={61-87} }

This paper concerns singular value decomposition (SVD)-based computable formulas and bounds for the condition number of the total least squares (TLS) problem. For the TLS problem with the coefficient matrix $$A$$ and the right-hand side $$b$$, a new closed formula is presented for the condition number. Unlike an important result in the literature that uses the SVDs of both $$A$$ and $$[A,\ b]$$, our formula only requires the SVD of $$[A,\ b]$$. Based on the closed formula, both lower and upper…

## 26 Citations

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It is shown that the condition numbers and perturbation bound of the TLS problem are unified in the ones of the MTLS problem.

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This paper is devoted to condition numbers of the total least squares problem with linear equality constraint (TLSE). With novel limit techniques, closed formulae for normwise, mixed and…

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For TLSE problems with equilibratory input data, numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution, while for sparse and badly scaled matrices, mixed and componentwise condition numbers-based estimations are much tighter.

### Sensitivity and Conditioning of the Truncated Total Least Squares Solution

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An explicit expression for the condition number of the truncated total least squares (TLS) solution of $Ax \approx b$ is presented using the notion of the Frechet derivative, and upper bounds are given, which are simple to compute and interpret.

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Konecker-product-based formulae for normwise, mixed and componentwise condition numbers of the minimum Frobenius norm TLSE solution are given and Compact upper bounds of these condition numbers are provided to reduce the storage and computation cost.

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In this paper, we show that the normwise condition number of the scaled total least squares problem can be transformed into a new and compact form. Considering the relationship between the scaled…

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