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Consortium of Swiss Academic Libraries

Linear barycentric rational quadrature

Klein, Georges ; Berrut, Jean-Paul

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

Université de Fribourg

The linear barycentric rational method for a class of delay Volterra integro-differential equations

Abdi, Ali ; Berrut, Jean-Paul ; Hosseini, Seyyed Ahmad

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...

Università della Svizzera italiana

Theory and applications of bijective barycentric mappings

Schneider, Teseo ; Hormann, Kai (Dir.)

Thèse de doctorat : Università della Svizzera italiana, 2017 ; 2017INFO007.

Barycentric coordinates provide a convenient way to represent a point inside a triangle as a convex combination of the triangle's vertices, and to linearly interpolate data given at these vertices. Due to their favourable properties, they are commonly applied in geometric modelling, finite element methods, computer graphics, and many other fields. In some of these applications it is desirable...

Consortium of Swiss Academic Libraries

On point spread function modelling: towards optimal interpolation

Bergé, Joel ; Price, Sedona ; Amara, Adam ; Rhodes, Jason

In: Monthly Notices of the Royal Astronomical Society, 2012, vol. 419, no. 3, p. 2356-2368

Consortium of Swiss Academic Libraries

On the Scalar Rational Interpolation Problem

ANTOULAS, A. C. ; ANDERSON, B. D. Q.

In: IMA Journal of Mathematical Control and Information, 1986, vol. 3, no. 2-3, p. 61-88

Università della Svizzera italiana

Analysis and new constructions of generalized barycentric coordinates in 2D

Anisimov, Dmitry ; Hormann, Kai (Dir.)

Thèse de doctorat : Università della Svizzera italiana, 2017 ; 2017INFO004.

Different coordinate systems allow to uniquely determine the position of a geometric element in space. In this dissertation, we consider a coordinate system that lets us determine the position of a two-dimensional point in the plane with respect to an arbitrary simple polygon. Coordinates of this system are called generalized barycentric coordinates in 2D and are widely used in computer...

Université de Fribourg

A new quasi-monte carlo technique based on nonnegative least squares and approximate Fekete points

Bittante, Claudia ; Marchi, Stefano De ; Elefante, Giacomo

In: Numerical Mathematics: Theory, Methods and Applications, 2016, vol. 9, no. 4, p. 640–663

The computation of integrals in higher dimensions and on general domains, when no explicit cubature rules are known, can be ”easily” addressed by means of the quasi- Monte Carlo method. The method, simple in its formulation, becomes computationally inefficient when the space dimension is growing and the integration domain is particularly complex. In this paper we present two new approaches...

Université de Fribourg

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...