The interval eigenvalue problem. (English) Zbl 0756.65056
Let \(A^ I\) be a quadratic interval matrix over \(R\). Then \(\lambda\in C\) is called an eigenvalue of \(A^ I\), if there exists a matrix \(A\in A^ I\) and a vector \(x\neq 0\) such that \(Ax=\lambda x\).
The paper is concerned with the set of eigenvalues of \(A^ I\), especially with bounds for them. The symmetric case is discussed first, and is then extended to the case of arbitrary interval matrices. Finally, connections with perturbation techniques are shown.
The paper is concerned with the set of eigenvalues of \(A^ I\), especially with bounds for them. The symmetric case is discussed first, and is then extended to the case of arbitrary interval matrices. Finally, connections with perturbation techniques are shown.
Reviewer: H.Ratschek (Düsseldorf)
MSC:
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 65G30 | Interval and finite arithmetic |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
Keywords:
interval eigenvalue problem; interval arithmetic; upper and lower bounds; linear interval equations; interval matrix; eigenvalueReferences:
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