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1.
M. Z. Garaev 《Mathematical Notes》2000,68(5-6):713-720
In the paper a method for finding lower bounds of the L
1-norm of some exponential sums is described. 相似文献
2.
In this paper, we formulate the l
p
-norm optimization problem as a conic optimization problem, derive its duality properties (weak duality, zero duality gap, and primal attainment) using standard conic duality and show how it can be solved in polynomial time applying the framework of interior-point algorithms based on self-concordant barriers. 相似文献
3.
Associated with the L
p
-curvature image defined by Lutwak, some inequalities for extended mixed p-affine surface areas of convex bodies and the support functions of L
p
-projection bodies are established. As a natural extension of a result due to Lutwak, an L
p
-type affine isoperimetric inequality, whose special cases are L
p
-Busemann-Petty centroid inequality and L
p
-affine projection inequality, respectively, is established. Some L
p
-mixed volume inequalities involving L
p
-projection bodies are also established. 相似文献
4.
We show that the minimum distance projection in the L
1-norm from an interior point onto the boundary of a convex set is achieved by a single, unidimensional projection. Application of this characterization when the convex set is a polyhedron leads to either an elementary minmax problem or a set of easily solved linear programs, depending upon whether the polyhedron is given as the intersection of a set of half spaces or as the convex hull of a set of extreme points. The outcome is an easier and more straightforward derivation of the special case results given in a recent paper by Briec (Ref. 1). 相似文献
5.
Approximation by Reciprocals of Polynomials with Positive Coefficients in L
p
Spaces 总被引:5,自引:0,他引:5
We prove that, if f(x) L
p
[0,1], 1 < p < , f(x) 0, x [0,1], f 0, then there is a polynomial p(x) +
n
such that f - 1/p
LP
C(p)(f,n
-1/2)
LP
where +
n
indicates the set of all polynomials of degree n with positive coeficients (see the definition (1) in the text). 相似文献
6.
P. A. Borodin 《Mathematical Notes》2007,82(5-6):725-732
For each p > 1, we obtain a lower bound for the distances to the real axis from the poles of simplest fractions (i.e., logarithmic derivatives of polynomials) bounded by 1 in the norm of L p on this axis; this estimate improves the first estimate of such kind derived by Danchenko in 1994. For p = 2, the estimate turns out to be sharp. Similar estimates are obtained for the distances from the poles of simplest fractions to the vertices of angles and rays. 相似文献
7.
Denis Larocque Serge Tardif Constance van Eeden 《Annals of the Institute of Statistical Mathematics》2000,52(3):488-506
The bivariate location problem is considered. The sup, L
1 and L
2 norms are used to construct bivariate sign tests from the univariate sign statistics computed on the projected observations on all lines passing through the origin. The tests so obtained are affine-invariant and distribution-free under the null hypothesis. The sup-norm gives rise to Hodges' test. A class of tests derived from the L
2-norm, with Blumen's test as a member, is seen to be related to a class proposed by Oja and Nyblom (1989, J. Amer. Statist. Assoc., 84, 249-259). The L
1-norm gives rise to a new test. Its asymptotic null distribution is seen to be the same as that of the L
1-norm of a certain normal process related to the standard Wiener process. An explicit expression of its cumulative distribution function is given. A simulation study will examine the merits of the three approaches. 相似文献
8.
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
9.
10.
11.
We prove L
r
estimates for the Dirichlet problem –div(a(x,u,Du))=f with f in L
q
for 1q+, where the operator satisfies (|s|)||
p
a(x,s,), with p>1. These estimates are obtained without symmetrization and are sharp in some cases. 相似文献
12.
13.
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
14.
D. Z. Marshan 《Mathematical Notes》2000,68(5-6):737-739
In this paper we study operators rearranging the Haar system in each bundle. It is proved that the norm of any nonidentical rearrangement admits a nontrivial lower bound in L
p spaces,
. 相似文献
15.
16.
Mathematical Notes - 相似文献
17.
A set of necessary conditions that must be satisfied by the L2 optimal rational transfer matrix approximating a given higher-order transfer matrix, is briefly described. On its basis, an efficient iterative numerical algorithm has been obtained and implemented using standard MATLAB functions. The purpose of this contribution is to make the related computer program available and to illustrate some significant applications.Work partially supported byConsorzio Padova Ricerche through the IRI programme Consortia Città Ricerche—Central European Initiative. 相似文献
18.
19.
It is shown that a Korovkin type theorem for a sequence of linear positive operators acting in weighted space L
p,w
(loc) does not hold in all this space and is satisfied only on some subspace. 相似文献
20.
研究了$(n+p)$维双曲空间$\mathbb{H}^{n+p}$中完备非紧子流形的第一特征值的上界.特别地,证明了$\mathbb{H}^{n+p}$中具有平行平均曲率向量$H$和无迹第二基本形式有限$L^q(q\geq n)$范数的完备子流形的第一特征值不超过$\frac{(n-1)^2(1-|H|^2)}{4}$,和$\mathbb{H}^{n+1}(n\leq5)$中具有常平均曲率向量$H$和无迹第二基本形式有限$L^q(2(1-\sqrt{\frac{2}{n}})
相似文献