In: Computer aided geometric design, 2021, vol. 88, p. 11
Bézier curves are indispensable for geometric modelling and computer graphics. They have numerous favourable properties and provide the user with intuitive tools for editing the shape of a parametric polynomial curve. Even more control and flexibility can be achieved by associating a shape parameter with each control point and considering rational Bézier curves, which comes with the...
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In: International journal on software tools for technology transfer, 2021, p. 15
The use of propositional logic and systems of linear inequalities over reals is a common means to model software for formal verification. Craig interpolants constitute a central building block in this setting for over-approximating reachable states, e.g. as candidates for inductive loop invariants. Interpolants for a linear system can be efficiently computed from a Simplex refutation by ...
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In: Advances in Computational Mathematics, 2015, vol. 41, no. 5, p. 1255-1288
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In: Designs, Codes and Cryptography, 2015, vol. 75, no. 2, p. 335-357
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In: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2015, vol. 56, no. 1, p. 351-371
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In: Communications in Mathematical Physics, 2015, vol. 335, no. 2, p. 571-608
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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: Journal of computational and applied mathematics, 2019, vol. 349, p. 292-301
Barycentric rational Floater–Hormann interpolants compare favourably to classical polynomial interpolants in the case of equidistant nodes, because the Lebesgue constant associated with these interpolants grows logarithmically in this setting, in contrast to the exponential growth experienced by polynomials. In the Hermite setting, in which also the first derivatives of the interpolant are...
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In: Journal of computational and applied mathematics, 2019, vol. 350, p. 114-129
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...
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