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Displaying 121 – 140 of 184

Optimal-order quadratic interpolation in vertices of unstructured triangulations

Josef Dalík (2008)

Applications of Mathematics

We study the problem of Lagrange interpolation of functions of two variables by quadratic polynomials under the condition that nodes of interpolation are vertices of a triangulation. For an extensive class of triangulations we prove that every inner vertex belongs to a local six-tuple of vertices which, used as nodes of interpolation, have the following property: For every smooth function there exists a unique quadratic Lagrange interpolation polynomial and the related local interpolation error...

Pointwise inequalities and approximation in fractional Sobolev spaces

David Swanson (2002)

Studia Mathematica

We prove that a function belonging to a fractional Sobolev space $L^{α, p} (ℝ ⁿ)$ may be approximated in capacity and norm by smooth functions belonging to $C^{m, λ} (ℝ ⁿ)$ , 0 < m + λ < α. Our results generalize and extend those of [12], [4], [14], and [11].

Pointwise inequalities for Sobolev functions and some applications

Bogdan Bojarski, Piotr Hajłasz (1993)

Studia Mathematica

We get a class of pointwise inequalities for Sobolev functions. As a corollary we obtain a short proof of Michael-Ziemer’s theorem which states that Sobolev functions can be approximated by $C^{m}$ functions both in norm and capacity.

Polya conditions for multivariate Birkhoff interpolation: from general to rectangular sets of nodes.

Crainic, M., Crainic, N. (2010)

Acta Mathematica Universitatis Comenianae. New Series

Polynomial approximation and $ω_{ϕ}^{r} (f, t)$ twenty years later.

Ditzian, Z. (2007)

Surveys in Approximation Theory (SAT)[electronic only]

Polynomial asymptotics and approximation of Sobolev functions

Piotr Hajłasz, Agnieszka Kałamajska (1995)

Studia Mathematica

We prove several results concerning density of $C_{0}^{\infty}$ , behaviour at infinity and integral representations for elements of the space $L^{m, p} = ⨍ | \nabla^{m} ⨍ \in L^{p}$ .

Quadratic spline quasi-interpolants on bounded domains of $ℝ^{d}, d = 1, 2, 3$ .

Sablonnière, P. (2003)

Rendiconti del Seminario Matematico

Quadrature of singular integrands over surfaces.

Atkinson, Kendall (2004)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Quadrature over the sphere.

Atkinson, Kendall, Sommariva, Alvise (2005)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Representation formulae for (C₀) m-parameter operator semigroups

Mi Zhou, George A. Anastassiou (1996)

Annales Polonici Mathematici

Some general representation formulae for (C₀) m-parameter operator semigroups with rates of convergence are obtained by the probabilistic approach and multiplier enlargement method. These cover all known representation formulae for (C₀) one- and m-parameter operator semigroups as special cases. When we consider special semigroups we recover well-known convergence theorems for multivariate approximation operators.

Shape-preserving multivariate polynomial approximation in $C {[- 1, 1]}^{m}$ .

Gal, Ciprian S., Gal, Sorin G. (2004)

International Journal of Mathematics and Mathematical Sciences

Solving a class of multivariate integration problems via Laplace techniques

Jean B. Lasserre, Eduardo S. Zeron (2001)

Applicationes Mathematicae

We consider the problem of calculating a closed form expression for the integral of a real-valued function f:ℝⁿ → ℝ on a set S. We specialize to the particular cases when S is a convex polyhedron or an ellipsoid, and the function f is either a generalized polynomial, an exponential of a linear form (including trigonometric polynomials) or an exponential of a quadratic form. Laplace transform techniques allow us to obtain either a closed form expression, or a series representation that can be handled...

Some tidbits on ideal projectors, commuting matrices and their applications.

Shekhtman, Boris (2009)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Spline Representations of Functions in Besov-Triebel-Lizorkin Spaces on Rn.

Winfried Sickel (1990)

Forum mathematicum

Stability of quadratic interpolation polynomials in vertices of triangles without obtuse angles

Josef Dalík (1999)

Archivum Mathematicum

An explicit description of the basic Lagrange polynomials in two variables related to a six-tuple $a^{1}, \dots, a^{6}$ of nodes is presented. Stability of the related Lagrange interpolation is proved under the following assumption: $a^{1}, \dots, a^{6}$ are the vertices of triangles $T_{1}, \dots, T_{4}$ without obtuse inner angles such that $T_{1}$ has one side common with $T_{j}$ for $j = 2, 3, 4$ .

Currently displaying 121 – 140 of 184

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Displaying 121 – 140 of 184

Optimal-order quadratic interpolation in vertices of unstructured triangulations

Pointwise inequalities and approximation in fractional Sobolev spaces

Pointwise inequalities for Sobolev functions and some applications

Polya conditions for multivariate Birkhoff interpolation: from general to rectangular sets of nodes.

Polynomial approximation and $ω_{ϕ}^{r} (f, t)$ twenty years later.

Polynomial asymptotics and approximation of Sobolev functions

Quadratic spline quasi-interpolants on bounded domains of $ℝ^{d}, d = 1, 2, 3$ .

Quadrature of singular integrands over surfaces.

Quadrature over the sphere.

Representation formulae for (C₀) m-parameter operator semigroups

Shape-preserving multivariate polynomial approximation in $C {[- 1, 1]}^{m}$ .

Solving a class of multivariate integration problems via Laplace techniques

Some tidbits on ideal projectors, commuting matrices and their applications.

Spline Representations of Functions in Besov-Triebel-Lizorkin Spaces on Rn.

Stability of quadratic interpolation polynomials in vertices of triangles without obtuse angles

Stable multiresolution analysis on triangles for surface compression.

Sur la construction de surfaces de classe $C^{k}$ à partir d’un grand nombre de données de Lagrange

Sur l’erreur d’interpolation des fonctions de plusieurs variables par les $D^{m}$ -splines

Sur les formules de quadrature numérique à nombre minimal de noeuds d'intégration.

Sur l’évaluation de l’erreur d’interpolation de Lagrange dans un ouvert de $ℝ^{n}$

Currently displaying 121 – 140 of 184