Bounds on real eigenvalues and singular values of interval matrices

Abstract

We study bounds on real eigenvalues of interval matrices, and our aim is to develop fast computable formulae that produce as-sharp-as-possible bounds. We consider two cases: general and symmetric interval matrices.

We focus on the latter case, since on the one hand such interval matrices have many applications in mechanics and engineering, and on the other hand many results from classical matrix analysis could be applied to them. We also provide bounds for the singular values of (generally nonsquare) interval matrices.

Finally, we illustrate and compare the various approaches by a series of examples.

Keywords

• interval matrix
• interval analysis
• real eigenvalue
• eigenvalue bounds
• singular value