1,720,967 research outputs found
Approximation of unbounded functions with linear positive operators
No full textElectrical Engineering, Mathematics and Computer Scienc
The Problem of A. F. Timan on the Precise Order of Decrease of the Best Approximations
No full textAbstractThe problem of Timan on finding a necessary and sufficient condition for Aσ(ƒ)Lq∼ωk(ƒ; 1/σ)Lq, σ → ∞, is solved. The condition is ωk(ƒ; δ)Lq ∼ ωk+1(ƒ; δ)Lq, δ → 0. Related problems in other situations have also been studied
Optimal Inputs for Approximate Linear Systems in Hilbert Spaces
No full textAbstractThe paper is a study of the problem of determining an optimal input given only an approximate linear model of an actual input-output system. The optimality criterion is the minimization of the maximal possible error in the output. Under the assumption that the input and the output spaces can be modeled as Hilbert spaces, complete results on the existence, uniqueness, and characterization of optimal inputs are obtained. The results culminate in an unconditionally convergent iterative algorithm for the optimal inputs
Total error in the discrete convolution backprojection algorithm in computerized tomography
No full textAbstractThe CBP algorithm in computerized tomography (CT) is a discrete realization of a well-known tool from approximation theory; namely, the approximation of a function f in Rn by its convolution with a (bandlimited) peaked kernel. The steps in a computer implementation (e.g., in medical CT scanners) of the algorithm evaluate an n-dimensional convolution by (a) interpolation of projection data (line integrals in a two-dimensional case), (b) a one-dimensional discrete convolution, and (c) interpolation of the convolved data, required in (d) a discrete backprojection (integration over a unit sphere). The total error in the algorithm is due to the discretization steps (a)–(d) and (e) the truncation error in the basic convolution approximation. In this work we augment the known error estimates for steps (b) and (b) with those for (a), (c) and (e) to arrive at a total error profile of the algorithm, which may be summarized as follows. In a discrete b-bandlimited CBP reconstruction fdb of f, under appropriate conditions in (a)–(e), the total error f − fdb is essentially of the order of ε(f, b) = supθϵSn−1∫[brvbar];σ[brvbar]b[brvbar]σ[brvbar]n−1[brvbar]f̂(σθ)[brvbar]dσ, b→∞
Lipschitz-Nikolskii constants and asymptotic simultaneous approximation of the Mn-operators. (Short Communication).
No full textLipschitz-Nikolskii constants and asymptotic simultaneous approximation of the Mn-operators.
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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