Related papers: Bivariate hierarchical Hermite spline quasi--inter…
Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to…
We study the local approximation properties in hierarchical spline spaces through multiscale quasi-interpolation operators. This construction suggests the analysis of a subspace of the classical hierarchical spline space (Vuong et al.,…
Roughly speaking, a near-best (abbr. NB) quasi-interpolant (abbr. QI) is an approximation operator of the form $Q_af=\sum_{\alpha\in A} \Lambda_\alpha (f) B_\alpha$ where the $B_\alpha$'s are B-splines and the $\Lambda_\alpha (f)$'s are…
This paper deals with Hermite osculatory interpolating splines. For a partition of a real interval endowed with a refinement consisting in dividing each subinterval into two small subintervals, we consider a space of smooth splines with…
The univariate spline quasi-interpolants (abbr. QIs) studied in this paper are approximation operators using B-spline expansions with coefficients which are linear combinations of discrete or weighted mean values of the function to be…
Subdivision surfaces are considered as an extension of splines to accommodate models with complex topologies, making them useful for addressing PDEs on models with complex topologies in isogeometric analysis. This has generated a lot of…
The library QIBSH++ is a C++ object oriented library for the solution of Quasi Interpolation problems. The library is based on a Hermite Quasi Interpolating operator, which was derived as continuous extensions of linear multistep methods…
The paper proposes a general quasi-interpolation scheme for high-dimensional function approximation. To facilitate error analysis, we view our quasi-interpolation as a two-step procedure. In the first step, we approximate a target function…
Univariate spline discrete quasi-interpolants (abbr. dQIs) are approximation operators using B-spline expansions with coefficients which are linear combinations of discrete values of the function to be approximated. When working with…
In this paper we derive approximate quasi-interpolants when the values of a function $u$ and of some of its derivatives are prescribed at the points of a uniform grid. As a byproduct of these formulas we obtain very simple approximants…
In this paper, we formally investigate two mathematical aspects of Hermite splines which translate to features that are relevant to their practical applications. We first demonstrate that Hermite splines are maximally localized in the sense…
We study local approximation properties in hierarchical spline spaces through a twofold approach. First, we design and analyze a robust adaptive refinement algorithm to construct locally graded meshes. Second, we establish rigorous…
In this paper, Hermite interpolation by parametric spline surfaces on triangulations is considered. The splines interpolate points, the corresponding tangent planes and normal curvature forms at domain vertices and approximate tangent…
In this paper, the construction of $C^{1}$ cubic quasi-interpolants on a three-direction mesh of $\RR^{2}$ is addressed. The quasi-interpolating splines are defined by directly setting their Bernstein-B\'{e}zier coefficients relative to…
We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from…
Given gridded cell-average data of a smooth multivariate function, we present a constructive explicit procedure for generating a high-order global approximation of the function. One contribution is the derivation of high order…
Continuous representations are fundamental for modeling sampled data and performing computations and numerical simulations directly on the model or its elements. To effectively and efficiently address the approximation of point clouds we…
Baskakov operators and their inverses can be expressed as linear differential operators on polynomials. Recurrence relations are given for the computation of these coefficients. They allow the construction of the associated Baskakov…
We describe a general approach for constructing a broad class of operators approximating high-dimensional curves based on geometric Hermite data. The geometric Hermite data consists of point samples and their associated tangent vectors of…
We study approximation properties of multivariate periodic functions from weighted Wiener spaces by sparse grids methods constructed with the help of quasi-interpolation operators. The class of such operators includes classical…