In this paper, a rigorous computational method to enclose eigenpairs of complex interval matrices is proposed. Each eigenpair is found by solving a nonlinear equation of the form via a contraction argument. The set-up of the method relies on the notion of , which provide an efficient mean of determining a domain on which the contraction mapping theorem is applicable.
We introduce a method to compute rigorous component-wise enclosures of discrete convolutions using the fast Fourier transform, the properties of Banach algebras, and interval arithmetic. The purpose of this new approach is to improve the implementation and the applicability of computer-assisted proofs performed in weighed Banach algebras of Fourier/Chebyshev sequences, whose norms are known to be numerically unstable. We introduce some application examples, in particular a rigorous aposteriori...
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...
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