共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we describe and analyze an algorithm for the fast computation of sparse wavelet coefficient arrays typically
arising in adaptive wavelet solvers. The scheme improves on an earlier version from Dahmen et al. (Numer. Math. 86, 49–101, 2000) in several respects motivated by recent developments of adaptive wavelet schemes. The new structure of the
scheme is shown to enhance its performance while a completely different approach to the error analysis accommodates the needs
put forward by the above mentioned context of adaptive solvers. The results are illustrated by numerical experiments for one
and two dimensional examples. 相似文献
2.
B?a?ej Wróbel 《Monatshefte für Mathematik》2012,168(1):125-149
By using amulti-dimensional analogue of the Mellin transform techniques we prove a multivariate multiplier theorem for general tensor product orthogonal expansions and a multivariate multiplier theorem for the Hankel transform. 相似文献
3.
We construct a wavelet basis on the unit interval with respect to which both the (infinite) mass and stiffness matrix corresponding to the one-dimensional Laplacian are (truly) sparse and boundedly
invertible. As a consequence, the (infinite) stiffness matrix corresponding to the Laplacian on the n-dimensional unit box with respect to the n-fold tensor product wavelet basis is also sparse and boundedly invertible. This greatly simplifies the implementation and
improves the quantitative properties of an adaptive wavelet scheme to solve the multi-dimensional Poisson equation. The results
extend to any second order partial differential operator with constant coefficients that defines a boundedly invertible operator. 相似文献
4.
In this paper, we consider the problem of the existence of general non-separable variate orthonormal compactly supported wavelet
basis when the symbol function has a special form. We prove that the general non-separable variate orthonormal wavelet basis
doesn't exist if the symbol function possesses a certain form. This helps us to explicate the difficulty of constructing the
non-separable variate wavelet basis and to hint how to construct non-separable variate wavelet basis.
This research is supported by the National Natural Science Foundation of China (No.69982002) and the Opening Foundation of
National Mobile Communications Research Laboratory in Southeast University. 相似文献
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We obtain Taylor approximations for functionals V?Tr(f(H0+V)) defined on the bounded self-adjoint operators, where H0 is a self-adjoint operator with compact resolvent and f is a sufficiently nice scalar function, relaxing assumptions on the operators made in [17], and derive estimates and representations for the remainders of these approximations. 相似文献
8.
We consider the multiple point evaluation problem for an n-dimensional space of functions [???1,1[ d ?? spanned by d-variate basis functions that are the restrictions of simple (say linear) functions to tensor product domains. For arbitrary evaluation points this task is faced in the context of (semi-)Lagrangian schemes using adaptive sparse tensor approximation spaces for boundary value problems in moderately high dimensions. We devise a fast algorithm for performing m?≥?n point evaluations of a function in this space with computational cost O(mlog d n). We resort to nested segment tree data structures built in a preprocessing stage with an asymptotic effort of O(nlog d???1 n). 相似文献
9.
F. Götze 《Probability Theory and Related Fields》1979,50(3):333-355
Summary A Berry-Essen result and asymptotic expansions are derived for the distribution of bivariate von Mises functionals under moment and smoothness conditions.The results apply to the Cramér-von Mises
2 — statistic as well as to the Central Limit Theorem in Hilbert space, yielding a convergence rate O(n
–1+) for every >0 on centered ellipsoids.Herrn Professor Dr. Leopold Schmetterer zu Ehren seines sechzigsten Geburtstages gewidmet 相似文献
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We study the approximation of compact linear operators defined over certain weighted tensor product Hilbert spaces. The information complexity is defined as the minimal number of arbitrary linear functionals needed to obtain an -approximation for the -variate problem which is fully determined in terms of the weights and univariate singular values. Exponential tractability means that the information complexity is bounded by a certain function that depends polynomially on and logarithmically on . The corresponding unweighted problem was studied in Hickernell et al. (2020) with many negative results for exponential tractability. The product weights studied in the present paper change the situation. Depending on the form of polynomial dependence on and logarithmic dependence on , we study exponential strong polynomial, exponential polynomial, exponential quasi-polynomial, and exponential -weak tractability with . For all these notions of exponential tractability, we establish necessary and sufficient conditions on weights and univariate singular values for which it is indeed possible to achieve the corresponding notion of exponential tractability. The case of exponential -weak tractability with is left for future study. The paper uses some general results obtained in Hickernell et al. (2020) and Kritzer and Woźniakowski (2019). 相似文献
12.
Jonas Ballani 《Numerische Mathematik》2012,121(3):433-460
In this paper, we propose a method for the fast evaluation of integrals stemming from boundary element methods including discretisations of the classical single and double layer potential operators. Our method is based on the parametrisation of boundary elements in terms of a d-dimensional parameter tuple. We interpret the integral as a real-valued function f depending on d parameters and show that f is smooth in a d-dimensional box. A standard interpolation of f by polynomials leads to a d-dimensional tensor which is given by the values of f at the interpolation points. This tensor may be approximated in a low rank tensor format like the (CP) format or the ${{\mathcal {H}}}$ -Tucker format. The tensor approximation has to be done only once and allows us to evaluate interpolants in ${{\mathcal{O}}(dr(m+1))}$ operations in the (CP) format, or ${{\mathcal{O}}(dk^3+dk(m+1))}$ operations in the ${{\mathcal H}}$ -Tucker format, where m denotes the interpolation order and the ranks r, k are small integers. We demonstrate that highly accurate integral values can be obtained at very moderate costs. 相似文献
13.
Eric Slud 《Probability Theory and Related Fields》1991,87(3):349-364
Summary This paper applies the stochastic calculus of multiple Wiener-Itô integral expansions to express the number of crossings of the mean level by a stationary (discrete- or continuous-time) Gaussian process within a fixed time interval [0,T]. The resulting expansions involve a class of hypergeometric functions, for which recursion and differential relations and some asymptotic properties are derived. The representation obtained for level-crossing counts is applied to prove a central limit theorem of Cuzick (1976) for level crossings in continuous time, using a general central limit theorem of Chambers and Slud (1989a) for processes expressed via multiple Wiener-Itô integral expansions in terms of a stationary Gaussian process. Analogous results are given also for discrete-time processes. This approach proves that the limiting variance is strictly positive, without additional assumptions needed by Cuzick.Research supported by Office of Naval Research contracts N00014-86-K-0007 and N00014-89-J-1051 相似文献
14.
It is well known that the-Walsh-Fourier expansion of a function from the block space ([0, 1 ) ), 1 <q≤∞, converges pointwise a.e. We prove that the same result is true for the expansion of a function from in certain periodixed smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of Lp-functions, 1<p<∞, converges in norm and pointwise almost everywhere. 相似文献
15.
Morten Nielsen 《逼近论及其应用》2002,18(1):34-50
It is well known that the-Walsh-Fourier expansion of a function from the block spaceB q([0,1]), 1
B q in certain periodized smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of Lp-functions, 1相似文献
16.
Backward stability of the Casteljau algorithm and two more efficient algorithms for polynomial tensor product surfaces with interest in CAGD is shown. The conditioning of the corresponding bases are compared. These algorithms are also compared with the corresponding Horner algorithm and their higher accuracy is shown. A running error analysis of the algorithms is also carried out providing algorithms which calculate “a posteriori” sharp error bounds simultaneously to the evaluation of the surface without increasing significantly the computational cost. 相似文献
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Doklady Mathematics - 相似文献
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Lorenzo Brandolese 《Proceedings of the American Mathematical Society》2005,133(11):3345-3353
We give a new characterization of a family of homogeneous Besov spaces by means of atomic decompositions involving poorly localized building blocks. Our main tool is an algorithm for expanding a wavelet into a series of dilated and translated Poisson kernels.