Estimations d'erreur pour des éléments finis droits presque dégénérés
Fast multilevel evaluation of smooth radial basis function expansions.
Fitting scattered data on spherelike surfaces using tensor products of trigonometric and polynomial splines.
From Taylor to quadratic Hermite-Padé polynomials.
General Haar systems and greedy approximation
We show that each general Haar system is permutatively equivalent in , 1 < p < ∞, to a subsequence of the classical (i.e. dyadic) Haar system. As a consequence, each general Haar system is a greedy basis in , 1 < p < ∞. In addition, we give an example of a general Haar system whose tensor products are greedy bases in each , 1 < p < ∞, d ∈ ℕ. This is in contrast to [11], where it has been shown that the tensor products of the dyadic Haar system are not greedy bases in for 1...
General Order Newton-Padé Approximants for Multivariate Functions.
Geometric data fitting.
Greedy approximation and the multivariate Haar system
We study nonlinear m-term approximation in a Banach space with regard to a basis. It is known that in the case of a greedy basis (like the Haar basis in , 1 < p < ∞) a greedy type algorithm realizes nearly best m-term approximation for any individual function. In this paper we generalize this result in two directions. First, instead of a greedy algorithm we consider a weak greedy algorithm. Second, we study in detail unconditional nongreedy bases (like the multivariate Haar basis in ,...
Harmonic interpolation based on Radon projections along the sides of regular polygons
Given information about a harmonic function in two variables, consisting of a finite number of values of its Radon projections, i.e., integrals along some chords of the unit circle, we study the problem of interpolating these data by a harmonic polynomial. With the help of symbolic summation techniques we show that this interpolation problem has a unique solution in the case when the chords form a regular polygon. Numerical experiments for this and more general cases are presented.
Ideal interpolation: Mourrain's condition vs. D-invariance
Mourrain [Mo] characterizes those linear projectors on a finite-dimensional polynomial space that can be extended to an ideal projector, i.e., a projector on polynomials whose kernel is an ideal. This is important in the construction of normal form algorithms for a polynomial ideal. Mourrain's characterization requires the polynomial space to be 'connected to 1', a condition that is implied by D-invariance in case the polynomial space is spanned by monomials. We give examples to show that, for more...
Integration over a Simplex, Truncated Cubes, and Eulerian Numbers.
Interpolation by bivariate polynomials based on Radon projections
For any given set of angles θ₀ < ... < θₙ in [0,π), we show that a set of Radon projections, consisting of k parallel X-ray beams in each direction , k = 0, ..., n, determines uniquely algebraic polynomials of degree n in two variables.
Interpolation by sums of radial functions.
Isomorphism of some anisotropic Besov and sequence spaces
An isomorphism between some anisotropic Besov and sequence spaces is established, and the continuity of a Stieltjes-type integral operator, acting on some of these spaces, is proved.
La Formula De Simpson Tridimensional.
Linear abhängige Punktfunktionale bei zweidimensionalen Interpolations- und Approximationsproblemen.
Localized polynomial bases on the sphere.
Matrix functions: Taylor expansion, sensitivity and error analysis
Mehrdimensionale Hermite-Interpolation und numerische Integration.
Methods for computing the least deviation from the sums of functions of one variable.