On the Construction of Multi-Dimensional Embedded Cubature Formulae.
On the control net of certain multivariate spline functions
On the least squares fit by radial functions to multidimensional scattered data.
On the local linear independence of translates of a box spline
On the order of approximation of functions by the bidimensional operators Favard-Szász-Mirakyan.
On the Uniform Norm of an Arbitrary Coefficient Functional over Finite Dimensional Subspaces of C (D).
Optimal Addition of Knots to Cubature Formulae for Planar Regions.
Optimal Cycles in Doubly Weighted Graphs and Approximation of Bivariate Functions by Univariate Ones.
Optimality of the range for which equivalence between certain measures of smoothness holds
Recently it was proved for 1 < p < ∞ that , a modulus of smoothness on the unit sphere, and , a K-functional involving the Laplace-Beltrami operator, are equivalent. It will be shown that the range 1 < p < ∞ is optimal; that is, the equivalence does not hold either for p = ∞ or for p = 1.
Optimal-order quadratic interpolation in vertices of unstructured triangulations
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...