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Summation of slowly convergent series

Walter Gautschi (1994)

Banach Center Publications

Among the applications of orthogonal polynomials described briefly on my previous visit to this Center [9, §3.2] were slowly convergent series whose terms could be represented in terms of the Laplace transform at integer arguments. We proposed to sum such series by means of Gaussian quadrature rules applied to suitable integrals involving weight functions of Einstein and Fermi type (cf. [13]). In the meantime it transpired that the technique is applicable to a large class of numerical series and,...

Three-dimensional reconstruction from projections

Jiří Jelínek, Karel Segeth, T. R. Overton (1985)

Aplikace matematiky

Computerized tomograhphy is a technique for computation and visualization of density (i.e. X- or γ -ray absorption coefficients) distribution over a cross-sectional anatomic plane from a set of projections. Three-dimensional reconstruction may be obtained by using a system of parallel planes. For the reconstruction of the transverse section it is necessary to choose an appropriate method taking into account the geometry of the data collection, the noise in projection data, the amount of data, the...

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