Journal ArticleDOI
Anwendung der Rechteckregel auf die reelle Hilberttransformation mit unendlichem Intervall
R. Kress,E. Martensen +1 more
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This article is published in Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik.The article was published on 1970-01-01. It has received 17 citations till now.read more
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Empirical orthogonal functions and related techniques in atmospheric science: A review
TL;DR: The basic theory of the main types of EOFs is reviewed, and a wide range of applications using various data sets are also provided.
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The Exponentially Convergent Trapezoidal Rule
TL;DR: It is shown that far from being a curiosity, the trapezoidal rule is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators.
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Computing the Hilbert transform on the real line
TL;DR: In this article, a collocation method based on an expansion in rational eigenfunctions of the Hilbert transform operator is proposed, which is implemented through the Fast Fourier Transform.
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A novel method for computing the Hilbert transform with Haar multiresolution approximation
TL;DR: Experimental results show that the proposed algorithm for computing the Hilbert transform based on the Haar multiresolution approximation outperforms the library function 'hilbert' in Matlab and is applied to compute the instantaneous phase of signals approximately.
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Numerical aspects of special functions
TL;DR: In this article, the authors describe methods that are important for the numerical evaluation of certain functions that frequently occur in applied mathematics, physics and mathematical statistics, such as recurrence relations, series expansions (both convergent and asymptotic), and numerical quadrature.
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The evaluation of integrals of the form
TL;DR: It is well known to computers that the approximate formulayields a surprising degree of accuracy even for quite large values of the interval h; for example, if h = 1 the error is one unit in the fourth decimal as discussed by the authors.