346 research outputs found

    Approximations to -, di- and tri- logarithms

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    We propose hypergeometric constructions of simultaneous approximations to polylogarithms. These approximations suit for computing the values of polylogarithms and satisfy 4-term Apery-like (polynomial) recursions.Comment: 11 pages, minor correction

    Best simultaneous approximation to totally bounded sequences in Banach spaces

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    This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.National Natural Science Foundation of ChinaProgram for New Century Excellent Talent in UniversityDirecci贸n General de Investigaci贸n Cient铆fica y T茅cnicaJunta de Andaluc铆

    Simultaneous sparse approximation via greedy pursuit

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    A simple sparse approximation problem requests an approximation of a given input signal as a linear combination of T elementary signals drawn from a large, linearly dependent collection. An important generalization is simultaneous sparse approximation. Now one must approximate several input signals at once using different linear combinations of the same T elementary signals. This formulation appears, for example, when analyzing multiple observations of a sparse signal that have been contaminated with noise. A new approach to this problem is presented here: a greedy pursuit algorithm called simultaneous orthogonal matching pursuit. The paper proves that the algorithm calculates simultaneous approximations whose error is within a constant factor of the optimal simultaneous approximation error. This result requires that the collection of elementary signals be weakly correlated, a property that is also known as incoherence. Numerical experiments demonstrate that the algorithm often succeeds, even when the inputs do not meet the hypotheses of the proof

    Dotson\u27s convexity, Banach operator pair and best simultaneous approximations

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    The existence of common fixed points is established for three mappings where T is either generalized (f,g)-nonexpansive or asymptotically (f,g)-nonexpansive on a set of fixed points which is not necessarily starshaped. As applications, the invariant best simultaneous approximation results are proved

    Best Simultaneous LpL^p Approximation in the "Sum" Norm

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    In this paper we consider best simultaneous approximation byalgebraic polynomials respect to the norm j=1kfjPp\sum_{j=1}^k\|f_j-P\|_p, 1\le p<\infty. We prove an interpolation propertyof the best simultaneous approximations and we study the structureof the set of cluster points of the best simultaneousapproximations on the interval [,],[-\epsilon,\epsilon], as 0\epsilon \to 0