共查询到20条相似文献,搜索用时 125 毫秒
1.
本文讨论了以第二类多项式Ua(x)的零点为插值节点的Hermite-Fejér插值算子Ha(f,x)及若干非一致收敛的Hermite-Fejér型插值算子在区间[-1,1]上关于权函数(1-x2)1/2的平均收敛问题.我们主要证得:当0
[-1,1]都有(?),并给出了收敛阶.此外也指明,当p=3时,该式对某些连续函数未必成立. 相似文献
2.
设X是桶空间,Y是序列完备的局部凸空间.本文证明了,由X到Y的紧算子组成的算子级数,其在弱算子拓扑下和一致算子拓扑下的子级数收敛是一致的,当且仅当(X’,β(X’,X))不拓扑同胚地包含CO;同时证明了,N’中σ(X’,X)-子级数收敛级数是β(X’;X)-子级数收敛的,当且仅当(X’,β(X’,X))不拓扑同胚地包含CO. 相似文献
3.
本文首先利用由两组具有局部最小支集的样条所组成的基函数,构造非均匀2 型三角剖分上二元三次样条空间S31,2(Δmn(2))的若干样条拟插值算子. 这些变差缩减算子由样条函数Bij1支集上5 个网格点或中心和样条函数Bij2支集上5 个网格点处函数值定义. 这些样条拟插值算子具有较好的逼近性,甚至算子Vmn(f) 能保持近最优的三次多项式性. 然后利用连续模,分析样条拟插值算子Vmn(f)一致逼近于充分光滑的实函数. 最后推导误差估计. 相似文献
4.
讨论了以第二类Tchebycheff多项式的零点为插值结点组的Grünwald插值于Lp下的收敛性.当1≤p<2时,给出了收敛速度的一个精确估计;当p≥2时,说明了其Lp下不是收敛算子列.给出了一种以第二类Tchebycheff多项式的零点为插值结点组的修改的Grünwald插值,证明了其于Lp(1≤p<∞)下是收敛的. 相似文献
5.
袁学刚 《纯粹数学与应用数学》2000,16(1):10-14
选取一组求和因子ρa,β构造了二重三角插值算子Fmn(f;y),使对于任意的f(x,y)∈C2π,2π都能在全面上一致收敛,且达到最佳收敛阶。 相似文献
6.
在本文中我们得到了一个比[1]中更好的P.Turán问题24的答案:若Hermite—Fejér插值过程对于任何f∈C[-1,1]都一致收敛,则定义于同一组节点上的Lagrange插值过程对于每个f∈{f:En(f)=o(n-(23)/(18)}都一致收敛,这里En(f)为f∈C[-1,1]的用次数≤n的代数多项式逼近的偏差. 相似文献
7.
《数学的实践与认识》2015,(10)
基于EQ_1~(rot)非协调矩形元及零阶R-T元对非线性抛物方程构造了一个新的混合元格式.利用EQ_1~(rot)元所具有的两个特殊性质:(I)插值算子与其投影算子是一致的;(II)当所考虑问题的精确解属于H~3(ΩΩ)时,其相容误差可以达到O(h~2)(h是剖分参数),比插值误差高一阶.同时借助关于这两个单元的高精度分析、平均值技巧和插值后处理技术,得到了关于原始变量以及通量的超逼近和整体超收敛结果. 相似文献
8.
史应光 《数学年刊A辑(中文版)》1992,(4)
本文给出了这样一个函数类:假如Hermite-Fejer 插值算子的范数具有阶n~δ,δ≥0,则它的Lagrange插值过程一致收敛(见P.Turan的第24个问题[1])。 相似文献
9.
10.
吴宗敏 《高校应用数学学报(A辑)》1991,6(3):331-336
Radial Basis插值是一种适用于多变量散乱数据的插值方法,有着广泛的应用.本文对函数f分析了用Hardy的inverse multiquadric进行Radial Basis插值当结点密集时的收敛阶.并找到了一族函数.对它们进行Radial Basis插值是连同各阶导数一致收敛的。 相似文献
11.
Shi Yingguang 《分析论及其应用》1991,7(4):28-39
Let Sn(f,x) be the Hermite-Fejér type interpolation satisfying Sn(f,xk)=f(xk), S′n(f,xk)=0, k=1,2,…,n and Sn(f,yi)=f(yi), j=1,2,…,m. For m=0, let Hn(f,x)≔Sn(f,x). This paper investigates relationship between Sn(f,x) and Hn(f,x), as well as, the saturation of Sn(f,x). 相似文献
12.
Let f∈C
[−1,1]
″
(r≥1) and Rn(f,α,β,x) be the generalized Pál interpolation polynomials satisfying the conditions Rn(f,α,β,xk)=f(xk),Rn
′(f,α,β,xk)=f′(xk)(k=1,2,…,n), where {xk} are the roots of n-th Jacobi polynomial Pn(α,β,x),α,β>−1 and {x
k
″
} are the roots of (1−x2)Pn″(α,β,x). In this paper, we prove that
holds uniformly on [0,1].
In Memory of Professor M. T. Cheng
Supported by the Science Foundation of CSBTB and the Natural Science Foundatioin of Zhejiang. 相似文献
13.
Bao Yongguang 《分析论及其应用》1995,11(4):15-23
Let ξn −1 < ξn −2 < ξn − 2 < ... < ξ1 be the zeros of the the (n−1)-th Legendre polynomial Pn−1(x) and −1=xn<xn−1<...<x1=1, the zeros of the polynomial
. By the theory of the inverse Pal-Type interpolation, for a function f(x)∈C
[−1,1]
1
, there exists a unique polynomial Rn(x) of degree 2n−2 (if n is even) satisfying conditions Rn(f, ξk) = f (εk) (1 ⩽ k ⩽ n −1); R1
n(f,xk)=f1(xk)(1≤k≤n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation
polynomial {Rn(f, x)} (n is even) and the main result of this paper is that if f∈C
[1,1]
r
, r≥2, n≥r+2, and n is even then |R1
n(f,x)−f1(x)|=0(1)|Wn(x)|h(x)·n3−r·E2n−r−3(f(r)) holds uniformly for all x∈[−1,1], where
. 相似文献
14.
Summary LetH
k,n
(f; x) be the polynomial which interpolates ak-times continously differentiable functionf as well as its derivatives up to the orderk at the Chebyshevnodes. An estimate of the norm ofH
k, n
(f) is obtained which enables an estimate of the error of interpolation in terms of arbitrary moduli of continuity off
(k)
. Furthermore, by a more general result on projection operators, it is shown thatH
k, n
(k)
(f; x) generally does not converge uniformly tof
(k)
. 相似文献
15.
A. K. Varma 《Israel Journal of Mathematics》1968,6(1):66-73
LetR
n(f; x) be a trigonometric polynomial of ordern satisfying Eqs. (1.1) and (1.2). The object of this note is to obtain sufficient conditions in order that thepth derivative ofR
n(f, x) converges uniformly tof
(p)(x) on the real line. The sufficient conditions turns out to bef
(p)(x) ∈ Lipα, α>0 with the restrictions of Eq. (1.3).
The author acknowledges financial support for this work from the University of Alberta, Post Doctoral Fellowship 1966–67.
The author is extremely grateful to the referee for pointing out some valuable results and suggestions. 相似文献
16.
Li Zhongkai 《分析论及其应用》1991,7(3):19-26
In this note we define a sequence {Ln(f;x)} of interpolatory polynomials based on a system xn={xkn, k=1,2,…n} of nodes to be a sequence of QLIP if for every f(x)∈C[−1,1], Ln(f; x) tends uniformly to f(x) and ρn=1+o(1) as n→∞, where ρn is the ratio of the number of points in xn, at which Ln(f;x) coincides with f(x), and the degree of Ln(f;x). Two sequences of QLIP are constructed, one of which is based on a Bernstein process and the other the Freud-Sharma's
construction. 相似文献
17.
LetP(x, A) be a transition probability on a measurable space (S, Σ) and letX n be the associated Markov chain.Theorem. Letf∈B(S, Σ). Then for anyx∈S we haveP x a.s. $$\mathop {\underline {\lim } }\limits_{n \to \infty } \frac{1}{n}\sum\limits_{k = 1}^n {f(X_k ) \geqslant } \mathop {\underline {\lim } }\limits_{n \to \infty } \mathop {\inf }\limits_{x \in S} \frac{1}{n}\sum\limits_{k = 1}^n {P^k f(x)} $$ and (implied by it) a corresponding inequality for the lim. If 1/n∑ k=1 n P k f converges uniformly, then for everyx∈S, 1/n ∑ k=1 n f(X k ) convergesP x a.s. Applications are made to ergodic random walks on amenable locally compact groups. We study the asymptotic behavior of 1/n∑ k=1 n μ k *f and of 1/n∑ k=1 n f(X k ) via that ofΨ n *f(x)=m(A n )?1∫ An f(xt), where {A n } is a Følner sequence, in the following cases: (i)f is left uniformly continuous (ii) μ is spread out (iii)G is Abelian. Non-Abelian Example: Let μ be adapted and spread-out on a nilpotent σ-compact locally compact groupG, and let {A n } be a Følner sequence. If forf∈B(G, ∑) m(A n )?1∫ An f(xt)dm(t) converges uniformly, then 1/n∑ k=1 n f(X k ) converges uniformly, andP x convergesP x a.s. for everyx∈G. 相似文献
18.
Suppose K is a closed convex nonexpansive retract of a real uniformly smooth Banach space E with P as the nonexpansive retraction. Suppose T : K → E is an asymptotically d-weakly contractive map with sequence {kn }, kn ≥ 1, lim kn = 1 and with F(T) n int (K) ≠ ø F(T):= {x ∈ K: Tx = x}. Suppose {x n } is iteratively defined by x n+1 = P((l ? knαn )x n +k n α n T(PT) n?l xn ), n = 1,2,...,x 1 ∈ K, where αn∈ (0,l) satisfies lim αn = 0 and Σαn = ∞. It is proved that {x n } converges strongly to some x * ∈ F(T)∩ int K. Furthermore, if K is a closed convex subset of an arbitrary real Banach space and T is, in addition uniformly continuous, with F(T) ≠ ø, it is proved that {xn } converges strongly to some x * ∈ F(T). 相似文献
19.
Yasuhiro Gotoh 《Journal d'Analyse Mathématique》2000,82(1):149-173
For a given growth functionH, we say that a domainD ?R n is anH-domain if δD x≤δD(x 0)H(k D(x,x 0)),x ∈D, where δD(x)=d(x?D) andk D denotes the quasihyperbolic distance. We show that ifH satisfiesH(0)=1, |H'|≤H, andH"≤H, then there exists an extremalH-domain. Using this fact, we investigate some fundamental properties ofH-domains. 相似文献
20.
M. Ivette Gomes 《Annals of the Institute of Statistical Mathematics》1984,36(1):71-85
Summary Let {X
n}n≧1 be a sequence of independent, identically distributed random variables. If the distribution function (d.f.) ofM
n=max (X
1,…,X
n), suitably normalized with attraction coefficients {αn}n≧1(αn>0) and {b
n}n≧1, converges to a non-degenerate d.f.G(x), asn→∞, it is of interest to study the rate of convergence to that limit law and if the convergence is slow, to find other d.f.'s
which better approximate the d.f. of(M
n−bn)/an thanG(x), for moderaten. We thus consider differences of the formF
n(anx+bn)−G(x), whereG(x) is a type I d.f. of largest values, i.e.,G(x)≡Λ(x)=exp (-exp(−x)), and show that for a broad class of d.f.'sF in the domain of attraction of Λ, there is a penultimate form of approximation which is a type II [Ф
α(x)=exp (−x−α), x>0] or a type III [Ψ
α(x)= exp (−(−x)α), x<0] d.f. of largest values, much closer toF
n(anx+bn) than the ultimate itself. 相似文献