In this paper we generate and study new cubature formulas based on spline quasi-interpolants defined as linear combinations of C bivariate quadratic B-splines on a rectangular domain Ω, endowed with a non-uniform criss-cross triangulation, with discrete linear functionals as coefficients. Such B-splines have their supports contained in Ω and there is no data point outside this domain. Numerical...

In this paper, we propose a method to deal with numerical integral by using two kinds of C quasi-interpolation operators on the bivariate spline space, and also discuss the convergence properties and error estimates. Moreover, the proposed method is applied to the numerical evaluation of 2-D singular integrals. Numerical experiments will be carried out and the results will be compared with some...

We show how to construct a stable hierarchical basis for piecewise quadratic C continuous splines defined on Powell–Sabin triangulations. We prove that this hierarchical basis is well suited for compressing surfaces. Our compression method does not require the construction of wavelets which are usually expensive to compute, but instead we construct a stable quasi-interpolation scheme for our sp...

Given a bivariate function f defined in a rectangular domain Ω, we approximate it by a C1 quadratic spline quasi-interpolant (QI) and we take partial derivatives of this QI as approximations to those of f. We give error estimates and asymptotic expansions for these approximations. We also propose a simple algorithm for the determination of stationary points, illustrated by a numerical example. ...

We give a recipe for deriving local spline approximation methods which reproduce the whole spline space. The methods are obtained by solving a series of local approximation problems. Examples of speci c quadratic and cubic approximation methods are given. x

A novel and efficient transform method for ECG data compression based on B-spline basis functions is proposed. The algorithm allows these basis functions to adapt their shape to the nonstationary behavior of ECG signals. The number and shape of these basis functions are completely characterized by the number and location of the so-called knots. The position of the knots can effectively be coded...

Sampling and reconstruction of generic multivariate functions is more efficient on non-Cartesian root lattices, such as the BCC (Body-Centered Cubic) lattice, than on the Cartesian lattice. We introduce a new n × n generator matrix A that enables, in n variables, for efficient reconstruction on the non-Cartesian root lattice An by a symmetric box-spline family M r . A2 is the hexagonal lattice ...