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Chordal Cubic Spline Quasi Interpolation
2012This paper studies cubic spline quasi-interpolation of parametric curves through sequences of points in any space dimension. We show that if the parameter values are chosen by chord length, the order of accuracy is four. We also use this chordal cubic spline quasi interpolant to approximate the arc length derivatives and the length of the parametric ...
Paul Sablonnière +2 more
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Near best refinable quasi-interpolants
Mathematics and Computers in Simulation, 2009Let \(\mathbb{Z}\) be the set of integers and \(n\geq2\) be fixed. The authors consider the class of linearly independent refinable functions \[ M_{n,h}:=\left\{ m_{n,h}(\cdot-k),k\in\mathbb{Z}\right\} , \] where \(m_{n,h}(x)\) has support \(\left[ -n,n\right] ,\) is centered at the origin and satisfies the refinement equation: \[ m_{n,h}(x)=\sum_{k=n}^
PELLEGRINO, ENZA, SANTI E.
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On Chebyshev-type discrete quasi-interpolants
Mathematics and Computers in Simulation, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Optimized Quasi-Interpolators for Image Reconstruction
IEEE Transactions on Image Processing, 2015We propose new quasi-interpolators for the continuous reconstruction of sampled images, combining a narrowly supported piecewise-polynomial kernel and an efficient digital filter. In other words, our quasi-interpolators fit within the generalized sampling framework and are straightforward to use.
Leonardo Sacht, Diego Nehab
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Tensioned Quasi-Interpolation Via Geometric Continuity
Advances in Computational Mathematics, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paola Lamberti, Carla Manni
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Quasi-Interpolants with Tension Properties from and in CAGD
Computing, 2004The authors present a method for constructing \(C^2\) quasi-interpolating schemes having tension properties.They discuss the applications of above schemes in the area of approximation of planar and spatial curves. The paper is organized in 5 sections.Section 1 contains a short presentation of the subject.Section 2 recalls the construction and the ...
MANNI, CARLA, PELOSI, FRANCESCA
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A family of Bernstein quasi-interpolants on [0,1]
Approximation Theory and its Applications, 1992The author introduces quasi-interpolants on \([0,1]\) that can be viewed as intermediate operators between the classical Bernstein operator and the Lagrange interpolation operator. These operators only use function values and derivative values of the Bernstein polynomial of a given function.
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A Hilbertian approach to quasi interpolation methods
Neural Parallel Sci. Comput., 2020An abstract approach to quasi-interpolation methods based on the Hilbertian theory of integral kernels is developed. The error estimates in the energy norm are obtained for the relevant quasi-interpolants. A new approximating operator adapted to the data function, satisfying given boundary conditions, is introduced.
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