We consider applications in which one needs to compute the (smooth) QR factorization of a fundamental matrix solution Y. Of course, for stability reasons, explicit computation of Y has to be avoided, and one seeks to compute the Q and R factors directly. Applications include approximation of Lyapunov exponents, continuous orthonormalization technique for solving two-point boundary value problems, and eigenvalue calculation (isospectral flow). Both analytical and numerical results are presented.

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