In this paper, we give error estimates for the weighted approximation of rmonotone functions on the real line with Freud weights by Bernstein-type operators.
This paper deals with the description and the representation of polynomials defined over n-simplices, The polynomials are computed by using two recurrent schemes: the Neville-Aitken one for the Lagrange interpolating ...This paper deals with the description and the representation of polynomials defined over n-simplices, The polynomials are computed by using two recurrent schemes: the Neville-Aitken one for the Lagrange interpolating operator and the De Casteljau one for the Bernstein-Bezier approximating operator. Both schemes fall intothe framework of transformations of the form where the F iare given numbers (forexample, at the initial step they coincide with the values of the function on a given lattice), and the coefficients (x) are linear polynomials valued in x and x is fixed. A general theory for such sequence of transformations can be found in [2] where it is also proved that these tranformations are completely characterized in term of a linear functional, reference functional. This functional is associated with a linear space., characteristic space.The concepts of reference functionals and characteristic spaces will be used and we shall prove the existence of a characteristic space for the reference functional: associated with these operators.展开更多
A two dimensional Bernstein operators on C(S) is given by B n(f;x,y)=nk=0kj=0f(jn,kn)P n,k,j (x,y) where S{(x,y)｜0≤x≤y≤1},f∈C(S),P n,k,j (x,y)=n kk jx j(y-x) k-j (1-y) n-k and the aproximation equivalence the...A two dimensional Bernstein operators on C(S) is given by B n(f;x,y)=nk=0kj=0f(jn,kn)P n,k,j (x,y) where S{(x,y)｜0≤x≤y≤1},f∈C(S),P n,k,j (x,y)=n kk jx j(y-x) k-j (1-y) n-k and the aproximation equivalence theorem is obtained.展开更多
基金Supported by the National Natural Science Foundation, 10601065
文摘In this paper, we give error estimates for the weighted approximation of rmonotone functions on the real line with Freud weights by Bernstein-type operators.
文摘This paper deals with the description and the representation of polynomials defined over n-simplices, The polynomials are computed by using two recurrent schemes: the Neville-Aitken one for the Lagrange interpolating operator and the De Casteljau one for the Bernstein-Bezier approximating operator. Both schemes fall intothe framework of transformations of the form where the F iare given numbers (forexample, at the initial step they coincide with the values of the function on a given lattice), and the coefficients (x) are linear polynomials valued in x and x is fixed. A general theory for such sequence of transformations can be found in [2] where it is also proved that these tranformations are completely characterized in term of a linear functional, reference functional. This functional is associated with a linear space., characteristic space.The concepts of reference functionals and characteristic spaces will be used and we shall prove the existence of a characteristic space for the reference functional: associated with these operators.
文摘A two dimensional Bernstein operators on C(S) is given by B n(f;x,y)=nk=0kj=0f(jn,kn)P n,k,j (x,y) where S{(x,y)｜0≤x≤y≤1},f∈C(S),P n,k,j (x,y)=n kk jx j(y-x) k-j (1-y) n-k and the aproximation equivalence theorem is obtained.
