Algorithms for cardinal interpolation using box splines and radial basis functions.
An algorithm for biparabolic spline
The paper deals with the computation of suitably chosen parameters of a biparabolic spline (ot the tensor product type) on a rectangular domain. Some possibilities of choosing such local parameters (concentrated, dispersed parameters) are discussed. The algorithms for computation of dispersed parameters (using the first derivative representation) and concentraced parameters (using the second derivative representation) are given. Both these algorithms repeatedly use the one-dimensional algorithms....
An Approximation Theorem for Integrable Harmonic Vector Fields.
An Implementation of the Method of Ermakov and Zolotukhin for Multidimensional Integration and Interpolation.
Analysis on the unit ball and on the simplex.
«Approximate approximations» and the cubature of potentials
The paper discusses new cubature formulas for classical integral operators of mathematical physics based on the «approximate approximation» of the density with Gaussian and related functions. We derive formulas for the cubature of harmonic, elastic and diffraction potentials approximating with high order in some range relevant for numerical computations. We prove error estimates and provide numerical results for the Newton potential.
Approximate smoothings of locally Lipschitz functionals
The paper deals with approximation of locally Lipschitz functionals. A concept of approximation, based on the idea of graph approximation of the generalized gradient, is discussed and the existence of such approximations for locally Lipschitz functionals, defined on open domains in , is proved. Subsequently, the procedure of a smooth normal approximation of the class of regular sets (containing e.g. convex and/or epi-Lipschitz sets) is presented.
Approximate solutions of equations defined by complex spherical multiplier operators.
Approximation by double Walsh polynomials.
Approximation by Hill functions. II.
Approximation in L... Sobolev Spaces on the 2-Sphere by Quasi-Interpolation.
Approximation of -Continuous and -Differentiable functions by GBS operators of Bernstein bivariate polynomials.
Approximation of -continuous and -differentiable functions by GBS operators defined by infinite sum.
Approximation of domains with Lipschitzian boundary
Approximation on the sphere by weighted Fourier expansions.
Approximation Power of Smooth Bivariate PP Functions.
Asymptotic estimates for best and stepwise approximation of convex bodies II.
Asyptotic Behaviour of Multiperiodic Functions G(x) = ... g (x/2...).
Attenuation Factors in Multivariate Fourier Analysis.
Best N-term approximation in electronic structure calculations I. One-electron reduced density matrix
We discuss best N-term approximation spaces for one-electron wavefunctions and reduced density matrices ρ emerging from Hartree-Fock and density functional theory. The approximation spaces for anisotropic wavelet tensor product bases have been recently characterized by Nitsche in terms of tensor product Besov spaces. We have used the norm equivalence of these spaces to weighted spaces of wavelet coefficients to proof that both and ρ are in for all with . Our proof is based on the...