6,403 research outputs found

    An Algorithm for the Real Interval Eigenvalue Problem

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    In this paper we present an algorithm for approximating the range of the real eigenvalues of interval matrices. Such matrices could be used to model real-life problems, where data sets suffer from bounded variations such as uncertainties (e.g. tolerances on parameters, measurement errors), or to study problems for given states. The algorithm that we propose is a subdivision algorithm that exploits so- phisticated techniques from interval analysis. The quality of the computed approximation, as well as the running time of the algorithm depend on a given input accuracy. We also present an efficient C++ implementation and illustrate its efficiency on various data sets. In most of the cases we manage to compute efficiently the exact boundary points (limited by floating point representation)

    H\"older Regularity of Geometric Subdivision Schemes

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    We present a framework for analyzing non-linear Rd\mathbb{R}^d-valued subdivision schemes which are geometric in the sense that they commute with similarities in Rd\mathbb{R}^d. It admits to establish C1,αC^{1,\alpha}-regularity for arbitrary schemes of this type, and C2,αC^{2,\alpha}-regularity for an important subset thereof, which includes all real-valued schemes. Our results are constructive in the sense that they can be verified explicitly for any scheme and any given set of initial data by a universal procedure. This procedure can be executed automatically and rigorously by a computer when using interval arithmetics.Comment: 31 pages, 1 figur
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