1,721,018 research outputs found
Numerical stability of fast trigonometric and orthogonal wavelet transforms
No full textFast trigonometric transforms and periodic orthogonal wavelet transforms are essential tools for numerous practical applications. It is very important that fast algorithms work stable in a floating point arithmetic. This survey paper presents recent results on the worst case analysis of roundoff errors occurring in floating point computation of fast Fourier transforms, fast cosine transforms, and periodic orthogonal wavelet transforms. All these algorithms realize matrix-vector products with unitary matrices. The results are mainly based on a factorization of a unitary matrix into a product of sparse, almost unitary matrices. It is shown that under certain conditions fast trigonometric and periodic orthogonal wavelet transforms can be remarkably stable
Numerical stability of fast trigonometric and orthogonal wavelet transforms
No full textFast trigonometric transforms and periodic orthogonal wavelet transforms are essential tools for numerous practical applications. It is very important that fast algorithms work stable in a floating point arithmetic. This survey paper presents recent results on the worst case analysis of roundoff errors occurring in floating point computation of fast Fourier transforms, fast cosine transforms, and periodic orthogonal wavelet transforms. All these algorithms realize matrix-vector products with unitary matrices. The results are mainly based on a factorization of a unitary matrix into a product of sparse, almost unitary matrices. It is shown that under certain conditions fast trigonometric and periodic orthogonal wavelet transforms can be remarkably stable
On the accuracy of surface spline interpolation on the unit sphere
No full textThis paper considers a novel modification to the surface splines that have previously been used on the unit sphere. The surface splines considered are a natural analogue of surface splines in IRd and possess a unique Fourier expansion in terms of an orthonormal basis of spherical harmonics. Knowing the decay of the associated Fourier coefficients is important because they enable error estimates for spherical interpolation. In this paper we explicitly compute the Fourier coefficients of the surface splines and employ a recent theoretical result [8] to provide a useful error bound. We illuminate our theoretical findings by performing numerical experiments on the sphere and also on the hemisphere
An extension of Montessus de Ballore's theorem on the convergence of interpolating rational functions
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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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