共查询到20条相似文献,搜索用时 250 毫秒
1.
Barvinok 《Foundations of Computational Mathematics》2008,2(4):393-412
Abstract. Let G be a compact group acting in a real vector space V . We obtain a number of inequalities relating the L
∞ norm of a matrix element of the representation of G with its L
2k
norm for a positive integer k . As an application, we obtain approximation algorithms to find the maximum absolute value of a given multivariate polynomial
over the unit sphere (in which case G is the orthogonal group) and for the assignment problem of degree d , a hard problem of combinatorial optimization generalizing the quadratic assignment problem (in which case G is the symmetric group). 相似文献
2.
Abstract. Subdivision with finitely supported masks is an efficient method to create discrete multiscale representations of smooth
surfaces for CAGD applications. Recently a new subdivision scheme for triangular meshes, called
-subdivision , has been studied. In comparison to dyadic subdivision, which is based on the dilation matrix 2I ,
-subdivision is based on a dilation M with det M=3 . This has certain advantages, for example, a slower growth for the number of control points.
This paper concerns the problem of achieving maximal sum rule orders for stationary
-subdivision schemes with given mask support, which is important because the sum rule order characterizes the order of the
polynomial reproduction, and provides an upper bound on the Sobolev smoothness of the surface. We study both interpolating
and approximating schemes for a natural family of symmetric mask support sets related to squares of sidelength 2n in Z
2
, and obtain exact formulas for the maximal sum rule order for arbitrary n . For approximating schemes, the solution is simple, and schemes with maximal sum rule order are realized by an explicit
family of schemes based on repeated averaging [15].
In the interpolating case, we use properties of multivariate Lagrange polynomial interpolation to prove the existence of
interpolating schemes with maximal sum rule orders. These can be found by solving a linear system which can be reduced in
size by using symmetries. From this, we construct some new examples of smooth (C
2
,C
3
) interpolating
-subdivision schemes with maximal sum rule order and symmetric masks. The construction of associated dual schemes is also
discussed. 相似文献
3.
Paul Sablonnière 《Advances in Computational Mathematics》2004,20(1-3):229-246
Bernstein bases, control polygons and corner-cutting algorithms are defined for C
1 Merrien's curves introduced in [7]. The convergence of these algorithms is proved for two specific families of curves. Results on monotone and convex interpolants which have been proved in [8] by Merrien and the author are also recovered. 相似文献
4.
Abstract. On a Banach space X consider an equibounded (C_0)-semigroup of linear operators { T(t): t ≥ 0} with infinitesimal generator A . We introduce fractional powers (-A)
α
, α >0 , of A with domain D((-A)
α
)) and characterize the K -functionals with respect to (X,D((-A)
α
)) via fractional differences [I-T(t)]
α
, via appropriate truncated hypersingular integrals and via some type of fractional integral over the resolvent of A . Immediate consequences are an abstract Marchaud-type inequality for moduli of smoothness arising from (semi-) groups of
operators as well as optimal and nonoptimal approximation results. 相似文献
5.
6.
Ying-guang Shi 《应用数学学报(英文版)》2002,18(2):277-288
Abstract
Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in the weighted L
p
norm on an arbitrary system of nodes are given.
Supported by the National Natural Sciences Foundation of China (No.19671082) 相似文献
7.
Abstract. We propose C 1 Hermite interpolants generated by the general subdivision scheme introduced by Merrien [17] and satisfying monotonicity or convexity constraints. For arbitrary values and slopes of a given function f at the end-points of a bounded interval, which are compatible with the contraints, the given algorithms construct shape-preserving interpolants. Moreover, these algorithms are quite simple and fast as well as adapted to CAGD. We also give error estimates in the case of interpolation of smooth functions. 相似文献
8.
Abstract. Let S be a finite set of points in general position in R
d
. We call a pair (A,B) of subsets of S an (i,j) -partition of S if |A|=i , |B|=j and there is an oriented hyperplane h with S
h=A and with B the set of points from S on the positive side of h . (i,j) -Partitions generalize the notions of k -sets (these are (0,k) -partitions) and j -facets ((d,j) -partitions) of point sets as well as the notion of i -faces of the convex hull of S ((i+1,0) -partitions). In oriented matroid terminology, (i,j) -partitions are covectors where the number of 0 's is i and the numbers of + 's is j .
We obtain linear relations among the numbers of (i,j) -partitions, mainly by means of a correspondence between (i-1) -faces of so-called k -set polytopes on the one side and (i,j) -partitions for certain j 's on the other side. We also describe the changes of the numbers of (i,j) -partitions during continuous motion of the underlying point set. This allows us to demonstrate that in dimensions exceeding
3 , the vector of the numbers of k -sets does not determine the vector of the numbers of j -facets—nor vice versa. Finally, we provide formulas for the numbers of (i,j) -partitions of points on the moment curve in R
d
. 相似文献
9.
Gabriele Nebe 《Journal of Algebra》2000,230(2):585
Let p > 2 be a prime, R =
p[ζpf − 1], K =
p[ζpf − 1], and G = SL2(pf). The group ring RG is calculated nearly up to Morita equivalence: The projections of RG into the simple components of KG are given explicitly and the endomorphism rings and homomorphism bimodules between the projective indecomposable RG-lattices are described. 相似文献
10.
Haase 《Semigroup Forum》2008,66(2):288-304
Abstract. We give necessary and sufficient conditions for an operator A on a Hilbert space to have a bounded H
∈
fty -calculus on a vertical strip symmetric to the imaginary axis. From this, a characterization of group generators on Hilbert
spaces is obtained yielding recent results of Liu and Zwart as corollaries. 相似文献
11.
Pierre Bousquet 《Journal d'Analyse Mathématique》2007,102(1):311-346
We are interested in the location of the singularities of maps u ∈ W
s,p
(S
N
, S
1) when 1 ≤ sp and 1 < sp < 2. To this end, we consider the distributional Jacobian. We show that the range of this operator on W
s,p
(S
N
, S
1) is the closure in W
s−2,p
⋂ W
−1,sp
of the set of N − 2-currents defined as the integration on smooth oriented N − 2-dimensional boundaryless submanifolds. 相似文献
12.
Werner Haußmann 《Journal of Mathematical Analysis and Applications》2007,331(2):840-849
In the present paper we will introduce a new approach to multivariate interpolation by employing polyharmonic functions as interpolants, i.e. by solutions of higher order elliptic equations. We assume that the data arise from C∞ or analytic functions in the ball BR. We prove two main results on the interpolation of C∞ or analytic functions f in the ball BR by polyharmonic functions h of a given order of polyharmonicity p. 相似文献
13.
Given two doubling measures μ and ν in a metric space (S, ρ) of homogeneous type, let B
0⊂S be a given ball. It has been a well-known result by now (see [1–4]) that the validity of an L
1→L
1 Poincaré inequality of the following form:
for all metric balls B⊂B
0⊂S, implies a variant of representation formula of fractional integral type: for ρ-a.e. x∈B
0,
One of the main results of this paper shows that an L
1 to L
q
Poincaré inequality for some 0 < q < 1, i.e.,
for all metric balls B⊂B
0, will suffice to imply the above representation formula. As an immediate corollary, we can show that the weak-type condition,
also implies the same formula.
Analogous theorems related to high-order Poincaré inequalities and Sobolev spaces in metric spaces are also proved.
Received December 27, 2000, Accepted May 28, 2001 相似文献
14.
Christiansen 《Constructive Approximation》2008,19(1):1-22
Abstract. We consider the indeterminate Stieltjes moment problem associated with the q -Laguerre polynomials. A transformation of the set of solutions, which has all the classical solutions as fixed points, is
established and we present a method to construct, for instance, continuous singular solutions. The connection with the moment
problem associated with the Stieltjes—Wigert polynomials is studied; we show how to come from q -Laguerre solutions to Stieltjes—Wigert solutions by letting the parameter α —> ∞ , and we explain how to lift a Stieltjes—Wigert solution to a q -Laguerre solution at the level of Pick functions. Based on two generating functions, expressions for the four entire functions
from the Nevanlinna parametrization are obtained. 相似文献
15.
Jiang 《Semigroup Forum》2008,67(1):50-62
Abstract.
We introduce a class of strongly E
*
-unitary inverse semigroups S
i
(G,P) (i=1,2) determined by a group G and a submonoid P of G and give an embedding theorem for S
i
(G,P) . Moreover we characterize 0 -bisimple strongly E
*
-unitary inverse monoids and 0 -bisimple strongly F
*
-inverse monoids by using S
i
(G,P) . 相似文献
16.
Joel Hass Rida T. Farouki Chang Yong Han Xiaowen Song Thomas W. Sederberg 《Advances in Computational Mathematics》2007,27(1):1-26
We describe a method that serves to simultaneously determine the topological configuration of the intersection curve of two
parametric surfaces and generate compatible decompositions of their parameter domains, that are amenable to the application
of existing perturbation schemes ensuring exact topological consistency of the trimmed surface representations. To illustrate
this method, we begin with the simpler problem of topology resolution for a planar algebraic curve F(x,y)=0 in a given domain, and then extend concepts developed in this context to address the intersection of two tensor-product
parametric surfaces p(s,t) and q(u,v) defined on (s,t)∈[0,1]2 and (u,v)∈[0,1]2. The algorithms assume the ability to compute, to any specified precision, the real solutions of systems of polynomial equations
in at most four variables within rectangular domains, and proofs for the correctness of the algorithms under this assumption
are given.
Mathematics subject classification (2000) 65D17 相似文献
17.
Schlosser 《Constructive Approximation》2008,19(2):163-178
Abstract. We give an r -dimensional generalization of H. S. Shukla's very-well-poised
8
ψ
8
summation formula. We work in the setting of multiple basic hypergeometric series very-well-poised over the root system
A
r-1
or, equivalently, the unitary group U(r) . Our proof, which is already new in the one-dimensional case, utilizes an A
r-1
nonterminating very-well-poised
6
φ
5
summation by S. C. Milne, a partial fraction decomposition, and analytic continuation. 相似文献
18.
ShanZhenLU GuiPingTAO 《数学学报(英文版)》2003,19(4):645-654
In this paper,the authors establish the weighted (L^p,L^q) estimates for a class of multilinear oscillatory singular integrals with smooth phases.Certain endpoint estimates are also considered. 相似文献
19.
《European Journal of Combinatorics》2002,23(8):1085
In this paper, we prove that if D is a 2- (v, k, 1) design withG ≤ Aut(D) block primitive and soc (G) = 2G2(q) then D is a Ree unital with parameters 2- (q3 + 1, q + 1, 1). 相似文献
20.
Ronald DeVore Guergana Petrova Vladimir Temlyakov 《Foundations of Computational Mathematics》2008,3(2):161-185
We study the approximation of a function class F in L
p
by choosing first a basis B and then using n -term approximation with the elements of B . Into the competition for best bases we enter all greedy (i.e., democratic and unconditional [20]) bases for L
p
. We show that if the function class F is well-oriented with respect to a particular basis B then, in a certain sense, this basis is the best choice for this type of approximation. Our results extend the recent results
of Donoho [9] from L
2
to L
p
, p\neq 2 . 相似文献