A Study On The Least Deviation From Zero Of Chebyshev Polynomials On A Curved Tetrahedron

The minimum zero deviation polynomial has important research value for the theory and application of the best approximation of the function,and the construction of the numerical quadrature formula.Based on the research on the properties of the generalized trigonometric function on the three-variables tetrahedron and the Chebyshev polynomial on the corresponding curved tetrahedron,this paper discusses the related issues of the minimum zero deviation polynomial on the curved tetrahedron.Firstly,the extreme value properties of the generalized cosine function HC4n,0,0-4n on the tetrahedron are discussed.On this basis,two types of high-precision quadrature formulas on the tetrahedron are con-structed by taking their extreme points as the integration nodes.Secondly,through the discussion of the extreme value properties of the Chebyshev polynomials Tn,o,n on the corresponding curved tetrahedrons,we get a kind of alternating in three-variables poly-nomial space,Furthermore,based on the multivariate Chebyshev theorem,the minimum zero deviation properties of Chebyshev polynomials are proved,and two types of high pre-cision quadrature formulas on the surface tetrahedron region in three-dimensional space are given.