In: Applied Mathematics Letters, 2020, vol. 103, p. 106196
In this work, we extend the so-called mapped bases or fake nodes approach to the barycentric rational interpolation of Floater–Hormann and to AAA approximants. More precisely, we focus on the reconstruction of discontinuous functions by the S-Gibbs algorithm introduced in De Marchi et al. (2020). Numerical tests show that it yields an accurate approximation of discontinuous functions.
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In: Applied Mathematics and Computation, 2020, vol. 371, p. 124924
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In: Numerical Algorithms, 2011, vol. 56, no. 1, p. 143-157
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In: Numerical Algorithms, 2007, vol. 45, no. 1-4, p. 369-374
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In: BIT Numerical Mathematics, 2012, vol. 52, no. 2, p. 407-424
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In: Journal of Scientific Computing, 2018, vol. 75, no. 3, p. 1757-1775
A method for solving delay Volterra integro-differential equations is introduced. It is based on two applications of linear barycentric rational interpolation, barycentric rational quadrature and barycentric rational finite differences. Its zero–stability and convergence are studied. Numerical tests demonstrate the excellent agreement of our implementation with the predicted convergence...
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In: Journal of Computational and Applied Mathematics, 2014, vol. 259, Part A, p. 95–107
Well-conditioned, stable and infinitely smooth interpolation in arbitrary nodes is by no means a trivial task, even in the univariate setting considered here; already the most important case, equispaced points, is not obvious. Certain approaches have nevertheless experienced significant developments in the last decades. In this paper we review one of them, linear barycentric rational...
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In: SIAM Journal on Scientific Computing, 2014, vol. 36, no. 1, p. A105–A123
We introduce two direct quadrature methods based on linear rational interpolation for solving general Volterra integral equations of the second kind. The first, deduced by a direct application of linear barycentric rational quadrature given in former work, is shown to converge at the same rate as the rational quadrature rule but is costly on long integration intervals. The second, based on a...
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In: SIAM Journal on Numerical Analysis, 2012, vol. 50, no. 2, p. 643–656
Derivatives of polynomial interpolants lead in a natural way to approximations of derivatives of the interpolated function, e.g., through finite differences. We extend a study of the approximation of derivatives of linear barycentric rational interpolants and present improved finite difference formulas arising from these interpolants. The formulas contain the classical finite differences as a...
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In: Bit Numerical Mathematics, 2012, vol. 52, no. 2, p. 407-424
Linear interpolation schemes very naturally lead to quadrature rules. Introduced in the eighties, linear barycentric rational interpolation has recently experienced a boost with the presentation of new weights by Floater and Hormann. The corresponding interpolants converge in principle with arbitrary high order of precision. In the present paper we employ them to construct two linear rational...
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