共查询到20条相似文献,搜索用时 234 毫秒
1.
Frances Y. Kuo Grzegorz W. Wasilkowski Henryk Wo
niakowski 《Journal of Approximation Theory》2008,152(2):135-160
We study the worst case setting for approximation of d variate functions from a general reproducing kernel Hilbert space with the error measured in the L∞ norm. We mainly consider algorithms that use n arbitrary continuous linear functionals. We look for algorithms with the minimal worst case errors and for their rates of convergence as n goes to infinity. Algorithms using n function values will be analyzed in a forthcoming paper.We show that the L∞ approximation problem in the worst case setting is related to the weighted L2 approximation problem in the average case setting with respect to a zero-mean Gaussian stochastic process whose covariance function is the same as the reproducing kernel of the Hilbert space. This relation enables us to find optimal algorithms and their rates of convergence for the weighted Korobov space with an arbitrary smoothness parameter α>1, and for the weighted Sobolev space whose reproducing kernel corresponds to the Wiener sheet measure. The optimal convergence rates are n-(α-1)/2 and n-1/2, respectively.We also study tractability of L∞ approximation for the absolute and normalized error criteria, i.e., how the minimal worst case errors depend on the number of variables, d, especially when d is arbitrarily large. We provide necessary and sufficient conditions on tractability of L∞ approximation in terms of tractability conditions of the weighted L2 approximation in the average case setting. In particular, tractability holds in weighted Korobov and Sobolev spaces only for weights tending sufficiently fast to zero and does not hold for the classical unweighted spaces. 相似文献
2.
In this paper, a characterization for an I(L)-topological space to be generated by a given co-tower of L-topological spaces is obtained. Moreover, the relationship between some properties of an I(L)-topological vector space generated by a co-tower of L-topological vector spaces and the corresponding properties of the given co-tower of L-topological vector spaces is investigated. Our results show that if an I(L)-topological vector space generated by a co-tower of L-topological vector spaces has some properties, such as local convexity and local boundedness, then all L-topological vector spaces in the co-tower also have the same properties. But the converse is incorrect even in the case of I-topological vector space generated by a co-tower of classical topological vector spaces. Finally, we supply a necessary and sufficient condition for an I(L)-topological vector space generated by a co-tower of L-topological vector spaces with some properties, such as local convexity and local boundedness, to have such properties too. 相似文献
3.
4.
Let π and π′ be automorphic irreducible cuspidal representations of GLm(QA) and GLm′(QA), respectively. Assume that π and π′ are unitary and at least one of them is self-contragredient. In this article we will give an unconditional proof of an orthogonality
for π and π′, weighted by the von Mangoldt function Λ(n) and 1−n/x. We then remove the weighting factor 1−n/x and prove the Selberg orthogonality conjecture for automorphic L-functions L(s,π) and L(s,π′), unconditionally for m≤4 and m′≤4, and under the Hypothesis H of Rudnick and Sarnak [20] in other cases. This proof of Selberg's orthogonality removes such
an assumption in the computation of superposition distribution of normalized nontrivial zeros of distinct automorphic L-functions by Liu and Ye [12]. 相似文献
5.
M. W. Müller 《Journal of Computational Analysis and Applications》2001,3(3):207-222
The optimal degree of approximation of the method of Gammaoperators G
n in L
p spaces is O(n
-1). In order to obtain much faster convergence, quasi-interpolants G
n
(k)
of G
n in the sense of Sablonnière are considered. We show that for fixed k the operator-norms G
n
(k)
p are uniformly bounded in n. In addition to this, for the first time in the theory of quasi-interpolants, all central problems for approximation methods (direct theorem, inverse theorem, equivalence theorem) could be solved completely for the L
p metric. Left Gamma quasi-interpolants turn out to be as powerful as linear combinations of Gammaoperators [6]. 相似文献
6.
Charles Audet Pierre Hansen Alejandro Karam Chi To Ng Sylvain Perron 《Optimization Letters》2008,2(4):483-495
We consider the problem of separating two sets of points in an n-dimensional real space with a (hyper)plane that minimizes the sum of L
p
-norm distances to the plane of points lying on the wrong side of it. Despite recent progress, practical techniques for the
exact solution of cases other than the L
1 and L
∞-norm were unavailable. We propose and implement a new approach, based on non-convex quadratic programming, for the exact
solution of the L
2-norm case. We solve in reasonable computing times artificial problems of up to 20000 points (in 6 dimensions) and 13 dimensions
(with 2000 points). We also observe that, for difficult real-life instances from the UCI Repository, computation times are
substantially reduced by incorporating heuristic results in the exact solution process. Finally, we compare the classification
performance of the planes obtained for the L
1, L
2 and L
∞ formulations. It appears that, despite the fact that L
2 formulation is computationally more expensive, it does not give significantly better results than the L
1 and L
∞ formulations. 相似文献
7.
Volker Krtschmer 《Fuzzy Sets and Systems》2002,130(3):1064
The classes of the Lp,∞- and Lp-metrics play an important role to develop a probability theory in fuzzy sample spaces. All of these metrics are known to be separable, but not complete. The classes are closely related as for each Lp,∞-metric there exists some Lp-metric which induces the same topology. This paper deals with the completion of the Lp,∞- and Lp-metrics. We can also show that the relationship between the classes of Lp,∞- and Lp-metrics still holds for the obtained respective classes of their completions. 相似文献
8.
J. L. Hayden 《Designs, Codes and Cryptography》1997,12(1):69-73
The paper studies a generalized Hadamard matrix H = (g
i
j) of order n with entries gi
j from a group G of order n. We assume that H satisfies: (i) For m k, G = {g
m
i
g
k
i
-1 i = 1,...., n} (ii) g
1i = g
i1 = 1 for each i; (iii) g
ij
-1 = g
ji for all i, j. Conditions (i) and (ii) occur whenever G is a(P, L) -transitivity for a projective plane of order n. Condition (iii) holds in the case that H affords a symmetric incidence matrix for the plane. The paper proves that G must be a 2-group and extends previous work to the case that n is a square. 相似文献
9.
10.
Jun Feng LI 《数学学报(英文版)》2005,21(6):1495-1508
In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some L^p(R^n) to L^p(R^n) when the m-th order derivatives of A belong to L^p(R^n) for r large enough. By this result, the author gets the estimates for the Sharp maximal functions of the multilinear operators with the m-th order derivatives of A being Lipschitz functions. It follows that the multilinear operators are (L^p, L^p)-type operators for 1 〈 p 〈 ∞. 相似文献
11.
For a normal variation of a hypersurface M
n
in a space form Q
c
n+1
by a normal vector field fN, R. Reilly proved:
where L
r
(0 < r < n – 1) is the linearized operator of the (r + 1)-mean curvature S
r+1 of Mn given by L
r
= div(P
r
); that is, L
r
= the divergence of the rth Newton transformation P
r
of the second fundamental form applied to the gradient , and L0 = the Laplacian of Mn.From the Dirichlet integral formula for L
r
new integral formulas are obtained by making different choices of f and g, generalizing known formulas for the Laplacian. The method gives a systematic process for proofs and a unified treatment for some Minkowski type formulas, via L
r
. 相似文献
12.
Jana Jurečková Roger Koenker A. H. Welsh 《Annals of the Institute of Statistical Mathematics》1994,46(4):737-755
We consider Jaeckel's (1971,Ann. Math. Statist.,42, 1540–1552) proposal for choosing the trimming proportion of the trimmed mean in the more general context of choosing a trimming proportion for a trimmedL-estimator of location. We obtain higher order expansions which enable us to evaluate the effect of the estimated trimming proportion on the adaptive estimator. We find thatL-estimators with smooth weight functions are to be preferred to those with discontinuous weight functions (such as the trimmed mean) because the effect of the estimated trimming proportion on the estimator is of ordern
–1 rather thann
–3/4. In particular, we find that valid inferences can be based on a particular smooth trimmed mean with its asymptotic standard error and the Studentt distribution with degrees of freedom given by the Tukey and McLaughlin (1963,Sankhy Ser. A,25, 331–352) proposal. 相似文献
13.
We construct a Rankin Selberg integral to represent the exterior cube L function L(,3,s) of an automorphic cuspidal module of GL6(
F
) (where F is a number field). We determine the poles of this L function and find period conditions for the special value L(,3,1/2). We use the Siegal Weil formula. We also state an analogue of the Gross–Prasad conjecture concerning a criterion for the nonvanishing of L(,3,1/2). 相似文献
14.
Let r
k
(n) denote the number of ways n can be expressed as a sum of k squares. Recently, S. Cooper (Ramanujan J. 6:469–490, [2002]), conjectured a formula for r
9(t), t≡5 (mod 8), r
11(t), t≡7 (mod 8), where t is a square-free positive integer. In this note we observe that these conjectures follow from the works of Lomadze (Akad.
Nauk Gruz. Tr. Tbil. Mat. Inst. Razmadze 17:281–314, [1949]; Acta Arith. 68(3):245–253, [1994]). Further we express r
9(t), r
11(t) in terms of certain special values of Dirichlet L-functions. Combining these two results we get expressions for these special values of Dirichlet L-functions involving Jacobi symbols.
相似文献
15.
Michael E. Picollelli 《Discrete Mathematics》2011,(20):2113
A 3-simplex is a collection of four sets A1,…,A4 with empty intersection such that any three of them have nonempty intersection. We show that the maximum size of a set system on n elements without a 3-simplex is for all n≥1, with equality only achieved by the family of sets containing a given element or of size at most 2. This extends a result of Keevash and Mubayi, who showed the conclusion for n sufficiently large. 相似文献
16.
For an n-simplex in H
n
or S
n
, we give sine theorems and their results for kth-order vertex angles which are defined in this paper. The Gram and edge matrices, and polar simplex of n-simplex in H
n
or S
n
are used to prove the theorems and their results. 相似文献
17.
L
p
approximation capability of radial basis function (RBF) neural networks is investigated. If g: R
+1 → R
1 and ∈ L
loc
p
(R
n
) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in L
p
(K) with any accuracy for any compact set K in R
n
, if and only if g(x) is not an even polynomial.
Partly supported by the National Natural Science Foundation of China (10471017) 相似文献
18.
Gabjin Yun 《Geometriae Dedicata》2002,89(1):133-139
Let M
n
, n 3, be a complete oriented immersed minimal hypersurface in Euclidean space R
n+1. We show that if the total scalar curvature on M is less than the n/2 power of 1/C
s
, where C
s
is the Sobolev constant for M, then there are no L
2 harmonic 1-forms on M. As corollaries, such a minimal hypersurface contains no nontrivial harmonic functions with finite Dirichlet integral and so it has only one end. This implies finally that M is a hyperplane. 相似文献
19.
Y. Ichihara 《Lithuanian Mathematical Journal》2008,48(2):188-202
We consider the sum of coefficients which are in the Dirichlet series expansion of symmetric square L-functions. In this paper, we obtain two estimates of this sum in weight and level aspects. These imply two estimates of the
sum of the n
2th Fourier coefficients of cusp forms. 相似文献
20.
We show that every n-point metric of negative type (in particular, every n-point subset of L
1) admits a Fréchet embedding into Euclidean space with distortion
, a result which is tight up to the O(log log n) factor, even for Euclidean metrics. This strengthens our recent work on the Euclidean distortion of metrics of negative
into Euclidean space.
S. Arora supported by David and Lucile Packard Fellowship and NSF grant CCR-0205594. J.R. Lee supported by NSF grant CCR-0121555,
NSF 0514993, NSF 0528414 and an NSF Graduate Research Fellowship. 相似文献