CONVEX POLYNOMIAL AND RIDGE APPROXIMATION OF LIPSCHITZ FUNCTIONS IN Rd

We consider classes of uniformly bounded convex Lipschitz functions defined on convex bodies in Rd, d ≥ 1, and obtain exact orders of approximation of these classes by convex polynomials in Lp, 1 ≤ p ≤ ∞. If d > 1, we also find exact orders of approximation by convex ridge functions in L₂....

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Bibliographic Details
Published in:The Rocky Mountain journal of mathematics 2010-01, Vol.40 (3), p.957-976
Main Authors: KONOVALOV, V.N., KOPOTUN, K.A., MAIOROV, V.E.
Format: Article
Language:English
Subjects:
Algebra
Approximation
Convexity
Degrees of polynomials
Mathematical functions
Mathematical inequalities
Mathematical theorems
Polynomials
Ridges
Online Access:Get full text
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Summary:We consider classes of uniformly bounded convex Lipschitz functions defined on convex bodies in Rd, d ≥ 1, and obtain exact orders of approximation of these classes by convex polynomials in Lp, 1 ≤ p ≤ ∞. If d > 1, we also find exact orders of approximation by convex ridge functions in L₂.
ISSN:0035-7596
1945-3795