In this paper sufficient conditions for mean convergence and rate of convergence of Hermite-Fejer type interpolation in the Lp norm on an arbitrary system of nodes are presented.
Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of fun...Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of function of class A(D) are presented. Moreover in general the order of approximation is sharp.展开更多
Provides information on a study which simplified and improved convergence of (0,1,2,3) interpolation on an arbitrary system of nodes. Definitions and notations; Results; Conjectures.
In this paper the uniform convergence of Hermite-Fejer interpolation and Griinwald type theorem of higher order on an arbitrary system of nodes are presented.
In this paper we obtain a complete solution to Problem 24 of P. Turan: If the Hermite-Fejer interpolation process converges for any f∈C[-1, 1], then the Lagrange interpolationprocess defined on the same nodes converg...In this paper we obtain a complete solution to Problem 24 of P. Turan: If the Hermite-Fejer interpolation process converges for any f∈C[-1, 1], then the Lagrange interpolationprocess defined on the same nodes converges for f∈Lipα with α?0.988.展开更多
The 'o' saturation theorem and the degree of Lwp, approximation by (0 - q' - q) type Hermite-Fejer interpolating polynomials for mean convergence are obtained.
Let X<sub>n</sub>={x<sub>kn</sub>=cosθ<sub>kn</sub>: θ<sub>kn</sub>=（kπ）/（n+1）, 1≤k≤n}be the node system which consists ofroots of U<sub>n</sub> （x...Let X<sub>n</sub>={x<sub>kn</sub>=cosθ<sub>kn</sub>: θ<sub>kn</sub>=（kπ）/（n+1）, 1≤k≤n}be the node system which consists ofroots of U<sub>n</sub> （x） =（sin（n+1）θ）/（sinθ）（x=cosθ θ∈[0,π]）, the second kind Chebyshevpolynomical. All the symbols below have the same meaning as Ref. [1]if notspecifically defined. We shall consider a kind of new interpolating problem in thisnote. For any non-negative integer q and f∈C[-1, 1], it is well known that thepolynomial Q<sub>nq</sub>（f）∈П<sub>N</sub> （N=2（q+1） （n+1） -1） satisfying the following conditions isuniquely determined:Q<sub>nq</sub>(f, x<sub>kn</sub>) =f(x<sub>kn</sub>), 1≤k≤n; Q<sub>nq</sub>（f,±1）=f（±1）,Q<sub>nq</sub><sup>j</sup>(f,x<sub>kn</sub>)=c<sub>jkn</sub>, 1≤k≤n,1≤j≤2q+1,Q<sub>nq</sub><sup>j</sup>（f,1）=d<sub>jn</sub>, Q<sub>nq</sub><sup>j</sup>（f,-1）=g<sub>jn</sub>, 1≤j≤q,where c<sub>jkn</sub>,d<sub>jn</sub>, g<sub>jn</sub>are any given real numbers. Q<sub>nq</sub>（f）is called the higher orderquasi Hermite-Fejer interpolation of f.We展开更多
In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,w...In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,we also get some other results about the mean approximation.展开更多
L' convergence of Hermite-Fejer interpolation and quasi-Hermite-Fejer interpolation based upon ze- ros of general orthogonal polynomials is investigated. This paper 'almost' characterizes such convergence ...L' convergence of Hermite-Fejer interpolation and quasi-Hermite-Fejer interpolation based upon ze- ros of general orthogonal polynomials is investigated. This paper 'almost' characterizes such convergence for all continuous functions.展开更多
基金Project 19671082 supported by National Natural Science Foundation of China, I acknowledge endless help from Prof. Shi Ying-Guang during finishing this paper.
文摘In this paper sufficient conditions for mean convergence and rate of convergence of Hermite-Fejer type interpolation in the Lp norm on an arbitrary system of nodes are presented.
文摘Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of function of class A(D) are presented. Moreover in general the order of approximation is sharp.
基金Project 19671082 Supported by National Natural Science Foundation of China.
文摘Provides information on a study which simplified and improved convergence of (0,1,2,3) interpolation on an arbitrary system of nodes. Definitions and notations; Results; Conjectures.
基金Project 2921200 Supported by National Natural Science Foundation of China.
文摘In this paper the uniform convergence of Hermite-Fejer interpolation and Griinwald type theorem of higher order on an arbitrary system of nodes are presented.
文摘In this paper we obtain a complete solution to Problem 24 of P. Turan: If the Hermite-Fejer interpolation process converges for any f∈C[-1, 1], then the Lagrange interpolationprocess defined on the same nodes converges for f∈Lipα with α?0.988.
基金This work is supported by the Doctor Foundation (No:02.T20102-06) and the Post Doctor Foundation of Ningbo University.
文摘The 'o' saturation theorem and the degree of Lwp, approximation by (0 - q' - q) type Hermite-Fejer interpolating polynomials for mean convergence are obtained.
文摘Let X<sub>n</sub>={x<sub>kn</sub>=cosθ<sub>kn</sub>: θ<sub>kn</sub>=（kπ）/（n+1）, 1≤k≤n}be the node system which consists ofroots of U<sub>n</sub> （x） =（sin（n+1）θ）/（sinθ）（x=cosθ θ∈[0,π]）, the second kind Chebyshevpolynomical. All the symbols below have the same meaning as Ref. [1]if notspecifically defined. We shall consider a kind of new interpolating problem in thisnote. For any non-negative integer q and f∈C[-1, 1], it is well known that thepolynomial Q<sub>nq</sub>（f）∈П<sub>N</sub> （N=2（q+1） （n+1） -1） satisfying the following conditions isuniquely determined:Q<sub>nq</sub>(f, x<sub>kn</sub>) =f(x<sub>kn</sub>), 1≤k≤n; Q<sub>nq</sub>（f,±1）=f（±1）,Q<sub>nq</sub><sup>j</sup>(f,x<sub>kn</sub>)=c<sub>jkn</sub>, 1≤k≤n,1≤j≤2q+1,Q<sub>nq</sub><sup>j</sup>（f,1）=d<sub>jn</sub>, Q<sub>nq</sub><sup>j</sup>（f,-1）=g<sub>jn</sub>, 1≤j≤q,where c<sub>jkn</sub>,d<sub>jn</sub>, g<sub>jn</sub>are any given real numbers. Q<sub>nq</sub>（f）is called the higher orderquasi Hermite-Fejer interpolation of f.We
文摘In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,we also get some other results about the mean approximation.
基金Supported by the National Natural Science Foundation of China.
文摘L' convergence of Hermite-Fejer interpolation and quasi-Hermite-Fejer interpolation based upon ze- ros of general orthogonal polynomials is investigated. This paper 'almost' characterizes such convergence for all continuous functions.
