1,720,984 research outputs found
A mixed interpolation-regression approximation operator on the triangle
Full text linkIn several applications, ranging from computational geometry and finite element analysis to computer graphics, there is a need to approximate functions defined on triangular domains rather than rectangular ones. For this purpose, frequently used interpolation methods include barycentric interpolation, piecewise linear interpolation, and polynomial interpolation. However, the use of polynomial interpolation methods may suffer from the Runge phenomenon, affecting the accuracy of the approximation in the presence of equidistributed data. In these situations, the constrained mock-Chebyshev least squares approximation on rectangular domains was shown to be a successful approximation tool. In this paper, we extend it to triangular domains, by using both Waldron and discrete Leja points. This paper is dedicated to Len Bos on the occasion of his retirement. Len, for us, is a master of mathematics and also a big friend. He introduced us to the fascinating world of "finding good interpolation no..
Numerical approximation of Fredholm integral equation by the constrained mock-Chebyshev least squares operator
Full text linkIn this paper, we propose two numerical approaches for approximating the solution of the following kind of integral equation f(y)−μ∫−11f(x)k(x,y)w(x)dx=g(y),y∈[−1,1],where f is the unknown solution, μ∈R∖{0}, k,g are given functions not necessarily known in the analytical form, and w is a Jacobi weight. The proposed projection methods are based on the constrained mock-Chebyshev least squares polynomials, and starting from data known at equally spaced points, provide a fine approximation of the solution. Such peculiarity can be helpful in all cases we deal with experimental data, typically measured at equispaced points. We prove the introduced methods are stable and convergent in some Sobolev subspace of C[−1,1]. Several numerical tests confirm the theoretical estimates and numerical effectiveness of the proposed method
An adaptive algorithm for determining the optimal degree of regression in constrained mock-Chebyshev least squares quadrature
Full text linkIn this paper we develop an adaptive algorithm for determining the optimal degree of regression in the constrained mock-Chebyshev least-squares interpolation of an analytic function to obtain quadrature formulas with high degree of exactness and accuracy from equispaced nodes. We numerically prove the effectiveness of the proposed algorithm by several examples
Product integration rules by the constrained mock-Chebyshev least squares operator
Full text linkIn this paper we consider the problem of the approximation of definite integrals on finite intervals for integrand functions showing some kind of "pathological" behavior, e.g. "nearly" singular functions, highly oscillating functions, weakly singular functions, etc. In particular, we introduce and study a product rule based on equally spaced nodes and on the constrained mock-Chebyshev least squares operator. Like other polynomial or rational approximation methods, this operator was recently introduced in order to defeat the Runge phenomenon that occurs when using polynomial interpolation on large sets of equally spaced points. Unlike methods based on piecewise approximation functions, mainly used in the case of equally spaced nodes, our product rule offers a high efficiency, with performances slightly lower than those of global methods based on orthogonal polynomials in the same spaces of functions. We study the convergence of the product rule and provide error estimates in subspaces of continuous functions. We test the effectiveness of the formula by means of several examples, which confirm the theoretical estimates
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
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Chylous Leakage After a Laparoscopic Live-Donor Nephrectomy: Case Report and Literature Review.
No full textDispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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