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Advances in Mathematics, 1978 Let \(\pi_m\) denote the class of all real polynomials of degree at most \(m\) and \(\pi_{m,n}\) denote the collection of all rational functions \(r_{m,n}(x)=\frac{p(x)}{q(x)}, p\in\pi_m, q\in\pi_n\). Let \(\lambda_{m,n}\equiv\lambda_{m,n}(f^{-1})=\inf_{r_{m,n}\in\pi_{m,n}}\left\|\frac1{f(x)}-\gamma_{m,n}(x)\right\|_{l_{\infty}[0,\infty]}\) where \(f\),
Erdös, Paul +2 more
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Generalized Hypergeometric Function 3F2 Ratios and Branched Continued Fraction Expansions
Axioms, 2021 The paper is related to the classical problem of the rational approximation of analytic functions of one or several variables, particulary the issues that arise in the construction and studying of continued fraction expansions and their multidimensional ...
Tamara Antonova +2 more
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Numerical integration for high order pyramidal finite elements [PDF]
, 2010 We examine the effect of numerical integration on the convergence of high order pyramidal finite element methods. Rational functions are indispensable to the construction of pyramidal interpolants so the conventional treatment of numerical integration ...
Nigam, Nilima, Phillips, Joel
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Fast and accurate con-eigenvalue algorithm for optimal rational approximations [PDF]
, 2012 The need to compute small con-eigenvalues and the associated con-eigenvectors of positive-definite Cauchy matrices naturally arises when constructing rational approximations with a (near) optimally small $L^{\infty}$ error. Specifically, given a rational
Beylkin, G., Haut, T. S.
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Detecting and diagnosing faults in dynamic stochastic distributions using a rational b-splines approximation to output PDFs [PDF]
, 2003 Describes the process of detecting and diagnosing faults in dynamic stochastic distributions using a rational b-splines approximation to output ...
G. A. Smook +16 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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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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On the closedness of approximation spectra [PDF]
, 2009 Generalizing Cusick's theorem on the closedness of the classical Lagrange spectrum for the approximation of real numbers by rational ones, we prove that various approximation spectra are closed, using penetration properties of the geodesic flow in cusp ...
Parkkonen, Jouni, Paulin, Frédéric
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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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