On the representation of functions and finite difference operators on adaptive dyadic grids.
On the Sensitivity of Orthogonal Polynomials to Perturbations in the Moments.
On the Sharpness of Theorems Concerning Zero-Free Regions for Certain Sequences of Polynomials.
On the singular decomposition of matrices.
On the smoothing spline regression models.
On the trapezoid quadrature formula and applications
On the two dimensional spline interpolation of Hermite-type.
On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals.
On the Variational Characterization and Convergence of Bivariate Splines.
On Unordering Horvitz and Thompson's Tl -Class of Linear Estimators.
On -manifolds and -surfaces for analysis of the convergence of mesh-based approximation.
On Weight Functions for Chebyshev Quadrature.
On weighted Ostrowski type inequalities for operators and vector-valued functions.
Operators approximating partial derivatives at vertices of triangulations by averaging
Let be a triangulation of a bounded polygonal domain , the space of the functions from linear on the triangles from and the interpolation operator from to . For a unit vector and an inner vertex of , we describe the set of vectors of coefficients such that the related linear combinations of the constant derivatives on the triangles surrounding are equal to for all polynomials of the total degree less than or equal to two. Then we prove that, generally, the values of the...
Optimal Addition of Knots to Cubature Formulae for Planar Regions.
Optimal Approximation and Error Bounds in Seminormed Spaces.
Optimal combined quadrature formulas in Schmeisser's sense.
Optimal Convergence of Minimum Norm Approximations in Hp.
Optimal cubature formulas in a reflexive Banach space
Sequences of cubature formulas with a joint countable set of nodes are studied. Each cubature formula under consideration has only a finite number of nonzero weights. We call a sequence of such kind a multicubature formula. For a given reflexive Banach space it is shown that there is a unique optimal multicubature formula and the sequence of the norm of optimal error functionals is monotonically decreasing to 0 as the number of the formula nodes tends to infinity.
Optimal Cycles in Doubly Weighted Graphs and Approximation of Bivariate Functions by Univariate Ones.