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Approximation by Rational Functions [PDF]
Proceedings of the American Mathematical Society, 1986 Making use of the Hardy-Littlewood maximal function, we give a new proof of the following theorem of Pekarski: If f ′ f’
R. DeVore
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Multivariate approximation by polynomial and generalized rational functions [PDF]
Optimization, 2021 In this paper, we develop an optimization-based approach to multivariate Chebyshev approximation on a finite grid. We consider two models: multivariate polynomial approximation and multivariate generalized rational approximation.
R. D. Millán +3 more
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Bounded approximation by rational functions. [PDF]
Pacific Journal of Mathematics, 1969 S. Fisher
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Approximation by rational functions
Applicable Analysis, 2008 The inverse problem of finding point sources from finite measurements of two-dimensional stationary field leads to the problem of interpolation by rational functions. However, unlike the polynomial interpolation, the system of equations for the polynomial coefficients appearing here is rather difficult to analyse and to solve numerically.
V. G. Cherednichenko
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Bounded approximation by rational functions. [PDF]
Pacific Journal of Mathematics, 1973 Theodore Gamelin, J. Garnett
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Full length article: Fractal rational functions and their approximation properties
Journal of Approximation Theory, 2014 An \(\alpha\)-fractal rational function is defined as the image of a rational function under the \(\alpha\)-fractal operator \(\mathcal F^{\alpha}\) (like \(\alpha\)-fractal polynomials from \textit{M. A. Navascués} [Z. Anal. Anwend. 24, No. 2, 401--418 (2005; Zbl 1082.28006)]).
P. Viswanathan, A. Chand
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On best rational approximation of analytic functions
Journal of Approximation Theory, 2005 The main result contained in this paper is described as follows. Let \(E\) be a compact set in the extended complex plane \(\overline{C}\), \(n\) be a nonnegative integer and \(f:E \to C\) be continuous. Let us consider the best rational approximation \(\rho_n(f,E)\) of \(f\) in the uniform metric \(\| \cdot - \cdot \| _E\) on \(E\) by the set \(R_n ...
exaly +4 more sources
Resolution of singularities by rational functions [PDF]
SIAM Journal on Numerical Analysis, 2023 Results on the rational approximation of functions containing singularities are presented. We build further on the ''lightning method'', recently proposed by Trefethen and collaborators, based on exponentially clustering poles close to the singularities.
Astrid Herremans +2 more
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Stokes flows in a two-dimensional bifurcation [PDF]
Royal Society Open ScienceThe flow network model is an established approach to approximate pressure–flow relationships in a bifurcating network, and has been widely used in many contexts.
Yidan Xue +2 more
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