论文信息 - Shape-preserving multivariate polynomial approximation in C[-1, 1]m

Shape-preserving multivariate polynomial approximation in C[-1, 1]m

We construct multivariate polynomials attached to a function f of m variables, m ≥ 2 , which approximate f with Jackson-type rate involving a multivariate Ditzian-Totik ω 2 φ -modulus and preserve some natural kinds of multivariate monotonicity and convexity of function. The result extends the bivariate case in Gal (2002), but does not follow straight from it and requires a careful calculation.

Sorin G. Gal | Ciprian S. Gal

[1] Pointwise estimates for convex polynomial approximation , 1986 .

[2] W Haussmann,et al. On the construction and convergence of multivariate interpolation operators , 1977 .

[3] Tibère Popoviciu. Sur quelques propriétés des fonctions d'une ou de deux variables réelles , 1933 .

[4] A. S. Shvedov. Orders of coapproximation of functions by algebraic polynomials , 1981 .

[5] V. Totik,et al. Moduli of smoothness , 1987 .

[6] G. Nürnberger. Approximation by Spline Functions , 1989 .

[7] Shape-preserving bivariate polynomial approximation inC([−1,1]×[−1,1]) , 2002 .