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Article

Castelli, Roberto ; Lessard, Jean-Philippe
A method to rigorously enclose eigenpairs of complex interval matrices. (English). In: Brandts, J., Korotov, S., Křížek, M., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2013, In honor of the 70th birthday of Karel Segeth. Proceedings. Prague, May 15-17, 2013. Institute of Mathematics AS CR, Prague, 2013. pp. 21-32
MSC: 15A42, 65F15, 65G30 | MR 3204427 | Zbl 1340.65057
Keywords:
eigenvalue; eigenvector; interval arithmetic; complex matrix
Summary:
In this paper, a rigorous computational method to enclose eigenpairs of complex interval matrices is proposed. Each eigenpair $x=(\lambda,\rv)$ 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 ${\em radii polynomials}$, which provide an efficient mean of determining a domain on which the contraction mapping theorem is applicable.
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