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Analytic enclosure of the fundamental matrix solution

Roberto Castelli;  Jean-Philippe Lessard;  Jason D. Mireles James — 2015

Applications of Mathematics

This work describes a method to rigorously compute the real Floquet normal form decomposition of the fundamental matrix solution of a system of linear ODEs having periodic coefficients. The Floquet normal form is validated in the space of analytic functions. The technique combines analytical estimates and rigorous numerical computations and no rigorous integration is needed. An application to the theory of dynamical system is presented, together with a comparison with the results obtained by computing...

A method to rigorously enclose eigenpairs of complex interval matrices

Castelli, Roberto;  Lessard, Jean-Philippe — 2013

Applications of Mathematics 2013

In this paper, a rigorous computational method to enclose eigenpairs of complex interval matrices is proposed. Each eigenpair x = ( λ , ) 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 r a d i i p o l y n o m i a l s , which provide an efficient mean of determining a domain on which the contraction mapping theorem is applicable.

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