Results 21 to 30 of about 283,081 (284)
A Rational Approximation for the Complete Elliptic Integral of the First Kind
Mathematics, 2020 Let K ( r ) be the complete elliptic integral of the first kind. We present an accurate rational lower approximation for K ( r ) . More precisely, we establish the inequality 2 π K ( r ) > 5 ( r ′ ) 2 + 126 r ′ + 61 61 (
Zhen-Hang Yang +2 more
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Density of rational points on isotrivial rational elliptic surfaces [PDF]
, 2011 For a large class of isotrivial rational elliptic surfaces (with section), we show that the set of rational points is dense for the Zariski topology, by carefully studying variations of root numbers among the fibers of these surfaces.
Anthony Várilly-Alvarado +14 more
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Advances in Mathematics, 1976 Several authors have investigated the question of approximating certain functions by reciprocals of polynomials under the uniform norm on the positive real axis. In this paper, the authors survey many of the known results in this direction. They also provide simplified proofs in some cases and obtain several new results as well.
Erdös, Paul, Reddy, A.R
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Algebraic Solution of Tropical Best Approximation Problems
Mathematics, 2023 We introduce new discrete best approximation problems, formulated and solved in the framework of tropical algebra, which deals with semirings and semifields with idempotent addition.
Nikolai Krivulin
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Compressed Passive Macromodeling [PDF]
, 2012 This paper presents an approach for the extraction of passive macromodels of large-scale interconnects from their frequency-domain scattering responses. Here, large scale is intended both in terms of number of electrical ports and required dynamic model ...
Grivet-Talocia, S. +1 more
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Rational approximation on spheres [PDF]
Israel Journal of Mathematics, 2015 We quantify the density of rational points in the unit sphere $S^n$, proving analogues of the classical theorems on the embedding of $\q^n$ into $\r^n$. Specifically, we prove a Dirichlet theorem stating that every point $ \in S^n$ is sufficiently approximable, the optimality of this approximation via the existence of badly approximable points, and a ...
Kleinbock, Dmitry, Merrill, Keith
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Parameter N Analysis on the Rational-Talbot Algorithm for Numerical Inversion of Laplace Transform
Vetor, 2021 This article investigates the numerical inversion of the Laplace Transform by the Rational-Talbot method and analyzes the influence on the variation of the free parameter N established by the technique when applied to certain functions.
Elisandra Freitas +4 more
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Frontiers in Applied Mathematics and Statistics, 2019 Rational filter functions can be used to improve convergence of contour-based eigensolvers, a popular family of algorithms for the solution of the interior eigenvalue problem. We present a framework for the optimization of rational filters based on a non-
Jan Winkelmann, Edoardo Di Napoli
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New Lower Bound for the Generalized Elliptic Integral of the First Kind
Mathematics, 2022 In this paper, we obtain a new simple rational approximation for Ka(r): the inequality 2Ka(r)/π>g2r′/g1r′ holds for all r∈(0,1), where Ka(r) is the generalized elliptic integral of the first kind, r′=1−r2, g1r′ and g2r′ are specific primary and quadratic
Ling Zhu
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Rational approximations of spectral densities based on the Alpha divergence
, 2013 We approximate a given rational spectral density by one that is consistent with prescribed second-order statistics. Such an approximation is obtained by minimizing a suitable distance from the given spectrum and under the constraints corresponding to ...
Zorzi, Mattia
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