Mathematics – Numerical Analysis
Scientific paper
2011-01-12
Mathematics
Numerical Analysis
Scientific paper
This paper concerns cheaply computable formulas and bounds for the condition number of the TLS problem. For a TLS problem with data $A$, $b$, two formulas are derived that are simpler and more compact than the known results in the literature. One is derived by exploiting the properties of Kronecker products of matrices. The other is obtained by making use of the singular value decomposition (SVD) of $[A \,\,b]$, which allows us to compute the condition number cheaply and accurately. We present lower and upper bounds for the condition number that involve the singular values of $[A \,\, b]$ and the last entries of the right singular vectors of $[A \,\, b]$. We prove that they are always sharp and can estimate the condition number accurately by no more than four times. Furthermore, we establish a few other lower and upper bounds that involve only a few singular values of $A$ and $[A \,\, b]$. We discuss how tight the bounds are. These bounds are particularly useful for large scale TLS problems since for them any formulas and bounds for the condition number involving all the singular values of $A$ and/or $[A \ b]$ are too costly to be computed. Numerical experiments illustrate that our bounds are sharper than a known approximate condition number in the literature.
Jia Zhongxiao
Li Bingyu
No associations
LandOfFree
A contribution to the condition number of the total least squares problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A contribution to the condition number of the total least squares problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A contribution to the condition number of the total least squares problem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-265019