1,720,966 research outputs found
Eigenvalue distributions of beta-Wishart matrices
Get PDFWe derive explicit expressions for the distributions of the extreme eigenvalues of the Beta-Wishart random matrices in terms of the hypergeometric function of a matrix argument. These results generalize the classical results for the real (β = 1), complex (β = 2), and quaternion (β = 4) Wishart matrices to any β > 0
Introduction to Numerical Methods
No full textThe focus of this course is on numerical linear algebra and numerical methods for solving ordinary differential equations. Topics include linear systems of equations, least square problems, eigenvalue problems, and singular value problems
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
Numerical Methods of Applied Mathematics II
No full textAdvanced introduction to applications and theory of numerical methods for solution of differential equations, especially of physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. Topics include finite differences, spectral methods, finite elements, well-posedness and stability, particle methods and lattice gases, boundary and nonlinear instabilities
Numerical Methods of Applied Mathematics II
No full textAdvanced introduction to applications and theory of numerical methods for solution of differential equations, especially of physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. Topics include finite differences, spectral methods, finite elements, well-posedness and stability, particle methods and lattice gases, boundary and nonlinear instabilities. From the course home page: Course Description This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods
Variations on the Author
Get PDF“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
Get PDFWe 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
Accurate eigenvalues of certain sign regular matrices
No full textAbstractWe present a new O(n3) algorithm for computing all eigenvalues of certain sign regular matrices to high relative accuracy in floating point arithmetic. The accuracy and cost are unaffected by the conventional eigenvalue condition numbers.A matrix is called sign regular when the signs of its nonzero minors depend only of the order of the minors. The sign regular matrices we consider are the ones which are nonsingular and whose kth order nonzero minors are of sign (-1)k(k-1)/2 for all k. This class of matrices can also be characterized as “nonsingular totally nonnegative matrices with columns in reverse order”.We exploit a characterization of these particular sign regular matrices as products of nonnegative bidiagonals and the reverse identity. We arrange the computations in such a way that no subtractive cancellation is encountered, thus guaranteeing high relative forward accuracy
Accurate SVDs of polynomial Vandermonde matrices involving orthonormal polynomials
No full textAbstractWe present a new O(n3) algorithm for computing the SVD of an n×n polynomial Vandermonde matrix VP=[Pi−1(xj)] to high relative accuracy in O(n3) time. The Pi are orthonormal polynomials, deg Pi=i, and xj are complex nodes. The small singular values of VP can be arbitrarily smaller than the largest ones, so that traditional algorithms typically compute them with no relative accuracy at all.We show that the singular values, even the tiniest ones, are usually well-conditioned functions of the data xj, justifying this computation.We also explain how this theory can be extended to other polynomial Vandermonde matrices, involving polynomials that are not orthonormal or even orthogonal
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