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11.
本文将在切触有理插值中起重要作用的Salzer定理推广到了多元向量的情形. 相似文献
12.
Deguang Han 《应用数学学报(英文版)》1994,10(2):213-219
In this paper we will prove some theorems on theM-ideals of compact operators and the best approximation of quasitriangular operator algebras. These results improve and extend the known results in [4, 5, 7].This work is supported in part by the National Natural Science Foundation of China. 相似文献
13.
Let E\subset \Bbb R
s
be compact and let d
n
E
denote the dimension of the space of polynomials of degree at most n in s variables restricted to E . We introduce the notion of an asymptotic interpolation measure (AIM). Such a measure, if it exists , describes the asymptotic behavior of any scheme τ
n
={ \bf x
k,n
}
k=1
dnE
, n=1,2,\ldots , of nodes for multivariate polynomial interpolation for which the norms of the corresponding interpolation operators do
not grow geometrically large with n . We demonstrate the existence of AIMs for the finite union of compact subsets of certain algebraic curves in R
2
. It turns out that the theory of logarithmic potentials with external fields plays a useful role in the investigation. Furthermore,
for the sets mentioned above, we give a computationally simple construction for ``good' interpolation schemes.
November 9, 2000. Date revised: August 4, 2001. Date accepted: September 14, 2001. 相似文献
14.
A Q-algebra can be represented as an operator algebra on an infinite dimensional Hilbert space. However we don’t know whether a finite n-dimensional Q-algebra can be represented on a Hilbert space of dimension n except n = 1, 2. It is known that a two dimensional Q-algebra is just a two dimensional commutative operator algebra on a two dimensional Hilbert space. In this paper we study a finite n-dimensional semisimple Q-algebra on a finite n-dimensional Hilbert space. In particular we describe a three dimensional Q-algebra of the disc algebra on a three dimensional Hilbert space. Our studies are related to the Pick interpolation problem for a uniform algebra. 相似文献
15.
一个稳定的补偿器可同时镇定n个对象(同时强镇定)等价于一个补偿器(不一定稳定)同时镇定n 1个对象(同时镇定).两个以上对象的同时强镇定和三个以上对象的伺时镇定是线性系统中一个急待解决的公开问题.文中所作的基本假定是所有的对象具有相同的简单不稳定零点,在此条件下给出了n个对象同时强镇定的一个充分条件.当仅有一个不稳定零点时.容易检验是否同时强镇定,否则仅需确定n个对象的不稳定零点并且判定由不稳定零点导出一个相应矩阵是正定的,就能判定n个对象同时强镇定.因此是一个易于检验的充分条件.文章同时给出了n个对象同时强镇定的算法,丰富了同时强镇定的充分条件. 相似文献
16.
In this paper we prove three conjectures of Revers on Lagrange interpolation for fλ(t)=|t|λ,λ>0, at equidistant nodes. In particular, we describe the rate of divergence of the Lagrange interpolants LN( fλ,t) for 0<|t|<1, and discuss their convergence at t=0. We also establish an asymptotic relation for max|t|1| |t|λ−LN( fλ,t)|. The proofs are based on strong asymptotics for |t|λ−LN( fλ,t), 0|t|<1. 相似文献
17.
For exponential weights, a necessary condition of weighted mean convergence for Lagrange interpolation is given. 相似文献
18.
Xin Tao YE Chong LI 《数学学报(英文版)》2007,23(1):65-76
The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided. 相似文献
19.
Arne Barinka Stephan Dahlke Wolfgang Dahmen 《Advances in Computational Mathematics》2006,24(1-4):5-34
Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work
balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations
as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the
approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could
be shown under the assumption that the entries in properly compressed standard representations are known or computable in
average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption
is justified in the context of elliptic boundary value problems.
Dedicated to Charles A. Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55.
This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported
in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The
second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract
HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1. 相似文献
20.
Carl Boor 《Advances in Computational Mathematics》2006,24(1-4):143-153
A lemma of Micchelli's, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary
linear functionals, as is Schaback's more recent extension of this lemma and Schaback's result concerning interpolation by
radial polynomials. Schaback's interpolant is explored.
Happy 60th and beyond, Charlie!
Mathematics subject classifications (2000) 41A05, 41A6. 相似文献