Approximation by polynomials composed of Weierstrass doubly periodic functions

Of Approximation by Polynomials to Continuous Functions

Approximation of multivariate periodic functions by trigonometric polynomials based on rank-1 lattice sampling

In this paper, we present algorithms for the approximation of multivariate periodic functions by trigonometric polynomials. The approximation is based on sampling of multivariate functions on rank-1 lattices. To this end, we study the approximation of periodic functions of a certain smoothness. Our considerations include functions from periodic Sobolev spaces of generalized mixed smoothness. Re...

APPROXIMATION OF 3D-PARAMETRIC FUNCTIONS BY BICUBIC B-SPLINE FUNCTIONS

In this paper we propose a method to approximate a parametric 3 D-function by bicubic B-spline functions

Approximation of Continuous Functions by Means of Lacunary Polynomials

be the orthonormal trigonometric sums on Di for weight p(6)cr(0) ; if the u's and v's are uniformly bounded on a point set D2 contained in Di, the same is true of the U's and Vs. For this case the proof admits a materially simpler formulation than when geometric configurations are contemplated having the degree of generality previously considered. The details relating to the loci C', C", K, K',...

Approximation of Gaussian by Scaling Functions and Biorthogonal Scaling Polynomials

The derivatives of the Gaussian function, G(x) = 1 √ 2π e−x 2/2, produce the Hermite polynomials by the relation, (−1)mG(m)(x) = Hm(x)G(x), m = 0, 1, . . . , where Hm(x) are Hermite polynomials of degree m. The orthonormal property of the Hermite polynomials, 1 m! ∫∞ −∞Hm(x)Hn(x)G(x)dx = δmn, can be considered as a biorthogonal relation between the derivatives of the Gaussian, {(−1)nG(n) : n = ...