Chebyshev Multivariate Polynomial Approximation: Alternance Interpretation

2018 ◽  
pp. 177-182 ◽  
Author(s):  
Nadezda Sukhorukova ◽  
Julien Ugon ◽  
David Yost
Keyword(s):  
Polynomial Approximation ◽  
Multivariate Polynomial

scholarly journals Shape-preserving multivariate polynomial approximation inC[−1,1]m

2004 ◽  
Vol 2004 (7) ◽  
pp. 325-333 ◽  
Author(s):  
Ciprian S. Gal ◽  
Sorin G. Gal
Keyword(s):  
Polynomial Approximation ◽  
Natural Kinds ◽  
Multivariate Polynomials ◽  
Jackson Type ◽  
Multivariate Polynomial ◽  
Shape Preserving ◽  
Bivariate Case ◽  
Type Rate

We construct multivariate polynomials attached to a functionfofmvariables,m≥2, which approximatefwith Jackson-type rate involving a multivariate Ditzian-Totikω2φ-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.

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