I would like to solve the least-squares for $\mathbf{Ax} = \mathbf{y}$ with some values in $\mathbf{A}$ and also in $\mathbf{y}$ are interval-valued numbers. In a more detail, e.g.,:
$$
\begin{bmatrix} a_{11} & a_{12} \\
a_{21} & \underline{\overline{a}}_{22} \\
a_{31} & a_{32}
\end{bmatrix} \begin{bmatrix} x_1 \\
x_2 &
\end{bmatrix} = \begin{bmatrix} y_1 \\
y_2 & \\
\underline{\overline{y}}_3 \\
\end{bmatrix}
$$
where $\underline{\overline{a}}_{22}$ means $\alpha_1 \le x_{22} \le \alpha_2$ and $\underline{\overline{y}}_3$ means $\beta_1 \le y_3\le \beta_2$, $\alpha_i,\beta_i\in\mathbb{R}$
The questions are:
- Is it possible to solve the equation above? I have found several papers that deal with square A, but not the case above
- Could anybody give clues or point references if the problem can be solved?
