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The four-point interpolatory scheme and the cubic B-spline are examples of the most well-known stationary subdivision procedures. They are based on the space of cubic polynomials and have their respective strengths and weaknesses. In this regard, ...

In this paper we propose an improvement of the classical Schoenberg-Marsden variation diminishing operator with applications to the construction of new quadrature rules that we show having better performances with respect to the already known ...

In this paper, the properties of quartic linear normal (LN) curves are studied. In particular, we present necessary and sufficient conditions for quartic LN curves to be regular. Using these conditions, we obtain an approximation ...

In this paper, we define a translation operator in a general form to allow for the application of the weighted harmonic mean in different applications. We outline the main steps to follow to define adapted methods using this tool. We ...

In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex ...

For h > 0 and positive integers m, d, such that m > d / 2, we study non-stationary interpolation at the points of the scaled grid h Z d via the Matérn kernel Φ m , d—the fundamental solution of ( 1 − Δ ) m in R d. We prove that the ...

• Use polynomials of Wachspress GBCs to construct smooth vertex splines over convex quadrilaterals.

In this paper we construct smooth bivariate spline functions over a polygonal partition, e.g. a convex quadrilateral partition by using vertex spline techniques. Vertex splines, introduced in Chui and Lai (1985) are smooth piecewise ...

The weighted essentially non-oscillatory schemes are well known for their shock captu- ring abilities due to their properties resulting from weighted combination reconstruction taken such that less weight is given to less smooth stencils. In this ...

The aim of this paper is to construct a new non-uniform corner-cutting (NUCC) subdivision scheme that improves the accuracy of the classical (stationary and non-stationary) methods. The refinement rules are formulated via the ...

Given a bivariate function and a finite rectangular grid, we perform transfinite interpolation at all the points on the grid lines. By noting the uniqueness of interpolation by rank-n functions, we prove that the result is identical to ...

In this paper we introduce a method for reconstruction of 3D objects from their 1D parallel cross-sections by set-valued interpolation. We regard a 3D object as the graph of a set-valued function defined on a planar domain, with the ...

The aim of this study is to present an improved third-order weighted essentially non-oscillatory (WENO) scheme for solving hyperbolic conservation laws. We first present a novel smoothness indicator by using discrete differential operator which ...

In this study, we present a new class of quasi-interpolatory non-stationary Hermite subdivision schemes reproducing exponential polynomials. This class extends and unifies the well-known Hermite schemes, including the interpolatory ...

A large class of multivariate quasi-projection operators is studied. These operators are sampling-type expansions ∑ k ∈ Z d c k ( f ) ψ ( A j · − k ) , where A is a matrix and the coefficients c_k (f) are associated with a ...

As specified by Little [7], the triangular Shepard method can be generalized to higher dimensions and to set of more than three points. In line with this idea, the hexagonal Shepard method has been recently introduced by combining six-points basis ...

The quality of the approximation of circular arcs by parametric polynomials is usually measured by the Hausdorff distance. It is sometimes important that a parametric polynomial approximant additionally preserves some particular ...

In this study, we present a new sixth-order finite difference weighted essentially non-oscillatory (WENO) scheme for solving Hamilton---Jacobi equations. The proposed scheme recovers the maximal approximation order in smooth regions without loss of ...

A class of rational quartic/cubic interpolation spline with two local control parameters is presented, which can be C2 continuous without solving a linear system of consistency equations for the derivative values at the knots. The effects of the local ...

In this paper we propose and analyze a new family of nonlinear subdivision schemes which can be considered non-oscillatory versions of the 6-point Deslauries-Dubuc (DD) interpolatory scheme, just as the Power p schemes are considered nonlinear non-...

Several properties of stationary subdivision schemes are nowadays well understood. In particular, it is known that the polynomial generation and reproduction capability of a stationary subdivision scheme is strongly connected with sum rules, its ...