An approximate method for the standard interval eigenvalue problem of real non-symmetric interval matrices (Q2721527)

Given a real \(n\times n\) interval matrix \(A^I= [\underline A,\overline A]\) and assuming that each \(A\in A^I\) has \(n\) distinct (not necessarily real) eigenvalues it is interesting to look for \(2n\) real intervals \(\lambda^I_{j,\text{Re}}\), \(\lambda^I_{j,\text{Im}}\), \(j= 1,\dots, n\), such that any eigenvalue \(\lambda= \lambda_{\text{Re}}+ i\lambda_{\text{Im}}\) of any matrix \(A\in A^I\) satisfies \(\lambda_{\text{Re}}\in \lambda^I_{j_0,\text{Re}}\), \(\lambda_{\text{Im}}\in \lambda^I_{j_0,\text{Im}}\) for some \(j_0\in \{1,\dots, n\}\). The authors recall a result due to \textit{A. S. Deif} in this respect [Z. Angew. Math. Mech. 71, No. 1, 61--64 (1991; Zbl 0756.65056)], and they apply first-order perturbation formulas in order to approach the problem of finding \(\lambda^I_{j,\text{Re}}\), \(\lambda^I_{j,\text{Im}}\), \(j= 1,\dots, n\). Two numerical examples, one of them resulting from an automobile suspension system, illustrate this approach.