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排序方式: 共有55条查询结果,搜索用时 15 毫秒
1.
Nonlinear Approximation by Trigonometric Sums 总被引:7,自引:0,他引:7
We investigate the
-error of approximation to a function
by a linear combination
of
exponentials
on
where the frequencies
are allowed to depend on
We bound this error in terms of the smoothness and other properties of
and show that our bounds are best possible in the sense of approximation of certain classes of functions. 相似文献
2.
We prove that forf∈L p , 0<p<1, andk a positive integer, there exists an algebraic polynomialP n of degree ≤n such that $$\left\| {f - P_n } \right\|_p \leqslant C\omega _k^\varphi \left( {f,\frac{1}{n}} \right)_p $$ whereω k ? (f,t)p is the Ditzian-Totik modulus of smoothness off inL p , andC is a constant depending only onk andp. Moreover, iff is nondecreasing andk≤2, then the polynomialP n can also be taken to be nondecreasing. 相似文献
3.
Near Best Tree Approximation 总被引:2,自引:0,他引:2
Baraniuk R.G. DeVore R.A. Kyriazis G. Yu X.M. 《Advances in Computational Mathematics》2002,16(4):357-373
Tree approximation is a form of nonlinear wavelet approximation that appears naturally in applications such as image compression and entropy encoding. The distinction between tree approximation and the more familiar n-term wavelet approximation is that the wavelets appearing in the approximant are required to align themselves in a certain connected tree structure. This makes their positions easy to encode. Previous work [4,6] has established upper bounds for the error of tree approximation for certain (Besov) classes of functions. This paper, in contrast, studies tree approximation of individual functions with the aim of characterizing those functions with a prescribed approximation error. We accomplish this in the case that the approximation error is measured in L
2, or in the case p2, in the Besov spaces B
p
0(L
p
), which are close to (but not the same as) L
p
. Our characterization of functions with a prescribed approximation order in these cases is given in terms of a certain maximal function applied to the wavelet coefficients. 相似文献
4.
Multiscale decompositions on bounded domains 总被引:6,自引:0,他引:6
A. Cohen W. Dahmen R. DeVore 《Transactions of the American Mathematical Society》2000,352(8):3651-3685
A construction of multiscale decompositions relative to domains is given. Multiscale spaces are constructed on which retain the important features of univariate multiresolution analysis including local polynomial reproduction and locally supported, stable bases.
5.
John J. Ambrosiano Scott T. Brandon Rainald Lhner C. Richard DeVore 《Journal of computational physics》1994,110(2)
Traditional techniques for computing electromagnetic solutions in the time domain rely on finite differences. These so-called FDTD (finite-difference time-domain) methods are usually defined only on regular lattices of points and can be too restrictive for geometrically demanding problems. Great geometric flexibility can be achieved by abandoning the regular latticework of sample points and adopting an unstructured grid. An unstructured grid allows one to place the grid points anywhere one chooses, so that curved boundaries can be fit with ease and local regions in which the field gradients are steep can be selectively resolved with a fine mesh. In this paper we present a technique for solving Maxwell's equations on an unstructured grid based on the Taylor-Galerkin finite-element method. We present several numerical examples which reveal the fundamental accuracy and adaptability of the method. Although our examples are in two dimensions, the techniques and results generalize readily to 3D. 相似文献
6.
Ronald DeVore Guergana Petrova Przemyslaw Wojtaszczyk 《Constructive Approximation》2011,33(1):125-143
Let f be a continuous function defined on Ω:=[0,1]
N
which depends on only ℓ coordinate variables, f(x1,?,xN)=g(xi1,?,xil)f(x_{1},\ldots,x_{N})=g(x_{i_{1}},\ldots,x_{i_{\ell}}). We assume that we are given m and are allowed to ask for the values of f at m points in Ω. If g is in Lip1 and the coordinates i
1,…,i
ℓ
are known to us, then by asking for the values of f at m=L
ℓ
uniformly spaced points, we could recover f to the accuracy |g|Lip1
L
−1 in the norm of C(Ω). This paper studies whether we can obtain similar results when the coordinates i
1,…,i
ℓ
are not known to us. A prototypical result of this paper is that by asking for C(ℓ)L
ℓ
(log 2
N) adaptively chosen point values of f, we can recover f in the uniform norm to accuracy |g|Lip1
L
−1 when g∈Lip1. Similar results are proven for more general smoothness conditions on g. Results are also proven under the assumption that f can be approximated to some tolerance ε (which is not known) by functions of ℓ variables. 相似文献
7.
The reaction of LiA1H4 with CO2 or NaHCO3 at elevated temperatures has been investigated. Methane and ethylene are the primary products of each reaction. These molecules are probably the “explosive” reaction products formed when CO2 fire extinguishers are used on LiAlH4 fires. 相似文献
8.
9.
As electronic operating frequencies increase toward the terahertz regime, new electrooptic modulators capable of low‐voltage high‐frequency operation must be developed to provide the necessary optical interconnects. This Letter presents a new concept that exploits modulation instability to compensate for the intrinsically weak electrooptic effect, χ(2). Simulations demonstrate more than 50 times enhancement of electrooptic effect at millimeter wave frequencies leading to a substantial reduction in the required modulation voltage.
10.
Pawel Bechler Ronald DeVore Anna Kamont Guergana Petrova Przemyslaw Wojtaszczyk 《Transactions of the American Mathematical Society》2007,359(2):619-635
Let be the space of functions of bounded variation on with . Let , , be a wavelet system of compactly supported functions normalized in , i.e., , . Each has a unique wavelet expansion with convergence in . If is the set of indicies for which are largest (with ties handled in an arbitrary way), then is called a greedy approximation to . It is shown that with a constant independent of . This answers in the affirmative a conjecture of Meyer (2001).