A method to rigorously enclose eigendecompositions of interval matrices
arXiv:1112.50523 citationsh-index: 41
Originality Incremental advance
AI Analysis
It provides a novel computational tool for verified numerical analysis of eigenvalue problems with interval uncertainties.
The paper proposes a rigorous method to enclose eigendecompositions of complex interval matrices using a contraction argument and radii polynomials, enabling verified computations.
In this paper, a rigorous computational method to enclose eigendecompositions of complex interval matrices is proposed. Each eigenpair $x=(λ,v)$ is found by solving a nonlinear equation of the form $f(x)=0$ via a contraction argument. The set-up of the method relies on the notion of radii polynomials, which provide an efficient mean of determining a domain on which the contraction mapping theorem is applicable.