The Degenerate Bounded Errors-in-Variables Model

Abstract

We consider the following problem: $\min_{x \in {\cal R}^n} \min_{\|E\| \le \eta} \|(A+E)x-b\|$, where $A$ is an $m \times n$ real matrix and $b$ is an $n$-dimensional real column vector when it has multiple global minima. This problem is an errors-in-variables problem, which has an important relation to total least squares with bounded uncertainty. A computable condition for checking if the problem is degenerate as well as an efficient algorithm to find the global solution with minimum Euclidean norm are presented.