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.
|
In: Applied Mathematics and Computation, 2020, vol. 371, p. 124924
|
In: Numerical Algorithms, 2011, vol. 56, no. 1, p. 143-157
|
In: Numerische Mathematik, 2009, vol. 112, no. 3, p. 341-361
|
In: Numerical Algorithms, 2007, vol. 45, no. 1-4, p. 369-374
|
In: BIT Numerical Mathematics, 2012, vol. 52, no. 2, p. 407-424
|
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...
|
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...
|
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...
|
Thèse de doctorat : Université de Fribourg, 2012 ; no. 1762.
This thesis is a collection of properties and applications of linear barycentric rational interpolation, mainly with the weights presented by Floater and Hormann in 2007. We are motivated by the counterintuitive and provable impossibility of constructing from equispaced data an approximation scheme that converges very rapidly to the approximated function and is simultaneously computationally...
|