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Barycentric rational interpolation with asymptotically monitored poles

Baltensperger, Richard

In: Numerical Algorithms, 2011, vol. 57, no. 1, p. 67-81

First applications of a formula for the error of finite sinc interpolation

Berrut, Jean-Paul

In: Numerische Mathematik, 2009, vol. 112, no. 3, p. 341-361

A formula for the error of finite sinc-interpolation over a finite interval

Berrut, Jean-Paul

In: Numerical Algorithms, 2007, vol. 45, no. 1-4, p. 369-374

Linear barycentric rational quadrature

Klein, Georges ; Berrut, Jean-Paul

In: BIT Numerical Mathematics, 2012, vol. 52, no. 2, p. 407-424

Numerical solution of boundary integral equations by means of attenuation factors

Reifenberg, M. ; Berrut, J-P

In: IMA Journal of Numerical Analysis, 2000, vol. 20, no. 1, p. 25-46

Recent advances in linear barycentric rational interpolation

Berrut, Jean-Paul ; Klein, Georges

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...

Confédéré : journal d'information du Valais romand

Martigny : Confédéré, 1861

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Linear barycentric rational quadrature

Klein, Georges ; Berrut, Jean-Paul

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...

A formula for the error of finite sinc-interpolation over a finite interval

Berrut, Jean-Paul

In: Numerical Algorithms, 2007, vol. 45, no. 1-4, p. 369-374

Sinc-interpolation is a very efficient infinitely differentiable approximation scheme from equidistant data on the infinite line. It, however, requires that the interpolated function decreases rapidly or is periodic. We give an error formula for the case where neither of these conditions is satisfied.

Optimized point shifts and poles in the linear rational pseudospectral method for boundary value problems

Berrut, Jean-Paul ; Mittelmann, Hans D.

In: Journal of Computational Physics, 2005, vol. 204, p. 292-301

Due to their rapid – often exponential – convergence as the number N of interpolation/collocation points is increased, polynomial pseudospectral methods are very efficient in solving smooth boundary value problems. However, when the solution displays boundary layers and/or interior fronts, this fast convergence will merely occur with very large N. To address this difficulty, we present a...