A note on the condition number of the scaled total least squares problem
For researchers working on total least squares problems, this provides more efficient condition number computation, though the contribution is incremental.
The paper derives simplified explicit expressions for the normwise condition number of the scaled total least squares problem, leading to new forms with storage and computational advantages. Three estimation methods are proposed and validated numerically.
In this paper, we consider the explicit expressions of the normwise condition number for the scaled total least squares problem. Some techniques are introduced to simplify the expression of the condition number, and some new results are derived. Based on these new results, new expressions of the condition number for the total least squares problem can be deduced as a special case. New forms of the condition number enjoy some storage and computational advantages. We also proposed three different methods to estimate the condition number. Some numerical experiments are carried out to illustrate the effectiveness of our results.