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1.
Barbara Bacchelli Mira Bozzini Christophe Rabut Maria-Leonor Varas 《Applied and Computational Harmonic Analysis》2005,18(3):516
In this paper, we build a multidimensional wavelet decomposition based on polyharmonic B-splines. The pre-wavelets are polyharmonic splines and so not tensor products of univariate wavelets. Explicit construction of the filters specified by the classical dyadic scaling relations is given and the decay of the functions and the filters is shown. We then design the decomposition/recomposition algorithm by means of downsampling/upsampling and convolution products. 相似文献
2.
On the construction of wavelets on a bounded interval 总被引:3,自引:0,他引:3
This paper presents a general approach to a multiresolution analysis and wavelet spaces on the interval [–1, 1]. Our method is based on the Chebyshev transform, corresponding shifts and the discrete cosine transformation (DCT). For the wavelet analysis of given functions, efficient decomposition and reconstruction algorithms are proposed using fast DCT-algorithms. As examples for scaling functions and wavelets, polynomials and transformed splines are considered. 相似文献
3.
We develop a stability and convergence analysis of Galerkin–Petrov schemes based on a general setting of multiresolution generated
by several refinable functions for the numerical solution of pseudodifferential equations on smooth closed curves. Particular
realizations of such a multiresolution analysis are trial spaces generated by biorthogonal wavelets or by splines with multiple
knots. The main result presents necessary and sufficient conditions for the stability of the numerical method in terms of
the principal symbol of the pseudodifferential operator and the Fourier transforms of the generating multiscaling functions
as well as of the test functionals. Moreover, optimal convergence rates for the approximate solutions in a range of Sobolev
spaces are established.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
4.
The purpose of this paper is to provide multiresolution analysis, stationary subdivision and pre-wavelet decomposition onL
2(R
d
) based on a general class of functions which includes polyharmonic B-splines.The work of this author has been partially supported by a DARPA grant.The work of this author has been partially supported by Fondo Nacional de Ciencia y Technologia under Grant 880/89. 相似文献
5.
Generalized cardinal B-splines are defined as convolution products of characteristic functions of self-affine lattice tiles
with respect to a given integer scaling matrix. By construction, these generalized splines are refinable functions with respect
to the scaling matrix and therefore they can be used to define a multiresolution analysis and to construct a wavelet basis.
In this paper, we study the stability and linear independence properties of the integer translates of these generalized spline
functions. Moreover, we give a characterization of the scaling matrices to which the construction of the generalized spline
functions can be applied. 相似文献
6.
Aurelian Bejancu 《Constructive Approximation》2011,34(2):237-256
Duchon’s method of thin plate splines defines a polyharmonic interpolant to scattered data values as the minimizer of a certain
integral functional. For transfinite interpolation, i.e., interpolation of continuous data prescribed on curves or hypersurfaces,
Kounchev has developed the method of polysplines, which are piecewise polyharmonic functions of fixed smoothness across the
given hypersurfaces and satisfy some boundary conditions. Recently, Bejancu has introduced boundary conditions of Beppo–Levi
type to construct a semicardinal model for polyspline interpolation to data on an infinite set of parallel hyperplanes. The
present paper proves that, for periodic data on a finite set of parallel hyperplanes, the polyspline interpolant satisfying
Beppo–Levi boundary conditions is in fact a thin plate spline, i.e., it minimizes a Duchon type functional. The construction
and variational characterization of the Beppo–Levi polysplines are based on the analysis of a new class of univariate exponential
ℒ-splines satisfying adjoint natural end conditions. 相似文献
7.
许兴业 《数学物理学报(A辑)》2003,(2)
该文以 Schauder- Tychonoff不动点定理为工具 ,建立了一类平面上带奇异性的非线性多重调和方程的正的径向对称整体解的存在性定理 ,并给出了解的有关性质 ,所得的结果丰富和发展文 [1 - 4]的结果 相似文献
8.
This paper introduces a domain decomposition preconditioner for
elliptic equations with rough coefficients. The coarse space of the
domain decomposition method is constructed via the so-called rough
polyharmonic splines (RPS for short). As an approximation space of
the elliptic problem, RPS is known to recover the quasi-optimal
convergence rate and attain the quasi-optimal localization property.
The authors lay out the formulation of the RPS based domain
decomposition preconditioner, and numerically verify the performance
boost of this method through several examples. 相似文献
9.
Desanka Radunović 《Numerical Algorithms》2008,47(2):191-210
The paper considers how cardinal exponential B-splines can be applied in solving singularly perturbed boundary problems. The
exponential nature and the multiresolution property of these splines are essential for an accurate simulation of a singular
behavior of some differential equation solutions. Based on the knowledge that the most of exponential B-spline properties
coincide with those of polynomial splines (smoothness, compact support, positivity, partition of unity, reconstruction of
polynomials, recursion for derivatives), one novel algorithm is proposed. It merges two well known approaches for solving
such problems, fitted operator and fitted mesh methods. The exponential B-spline basis is adapted for an interval because
a considered problem is solved on a bounded domain.
相似文献
10.
Matthew J. Hirn 《Proceedings of the American Mathematical Society》2008,136(3):899-908
Refinable functions have been widely investigated because of their importance in wavelet theory and multiresolution analysis, as well as because of intrinsic interest. Problems involving refinability can be challenging and interesting problems in mathematics. Several papers have investigated refinability of splines and other classes of functions. The purpose of this paper is to develop necessary and sufficient conditions for the refinability of the class of step functions on the real line taking complex values.
11.
许兴业 《数学物理学报(A辑)》2003,23(2):175-182
该文以Schauder-Tychonoff不动点定理为工具,建立了一类平面上带奇异性的非线性 多重调和方程的正的径向对称整体解的存在性定理,并给出了解的有关性质,所得的结果丰 富和发展文[1][4]的结果。 相似文献
12.
关于具局部插值性质的样条 总被引:11,自引:0,他引:11
引言 插值样条作为逼近工具有许多优点,但也受到一些限制。例如大部分样条都只限于多项式样条。又如样条插值带有整体性,即一插值点上的任何变化将波及整个样条的所有各点。此外高阶样条的计算较复杂。 本文给出一种新的构造样条的方法,它将不限于多项式样条,并且主要是它具有局部插值性,即这种样条在一个子区间上的值只与其邻近的几个插值点有关。我们称这种样条为局部插值样条。 与通常的多项式样条相比,局部样条的计算比较简单,并且一个插值点上的数值变动只影响其邻近的局部范围。 相似文献
13.
M. J. Johnson 《Constructive Approximation》1997,13(2):155-176
An upper bound on theL
p-approximation power (1 ≤p ≤ ∞) provided by principal shift-invariant spaces is derived with only very mild assumptions on the generator. It applies
to both stationary and nonstationary ladders, and is shown to apply to spaces generated by (exponential) box splines, polyharmonic
splines, multiquadrics, and Gauss kernel. 相似文献
14.
Lawrence W. Baggett Jennifer E. Courter Kathy D. Merrill 《Applied and Computational Harmonic Analysis》2002,13(3):201
The classical constructions of wavelets and scaling functions from conjugate mirror filters are extended to settings that lack multiresolution analyses. Using analogues of the classical filter conditions, generalized mirror filters are defined in the context of a generalized notion of multiresolution analysis. Scaling functions are constructed from these filters using an infinite matrix product. From these scaling functions, non-MRA wavelets are built, including one whose Fourier transform is infinitely differentiable on an arbitrarily large interval. 相似文献
15.
Mario Kapl 《Journal of Computational and Applied Mathematics》2009,231(2):828-839
We construct biorthogonal spline wavelets for periodic splines which extend the notion of “lazy” wavelets for linear functions (where the wavelets are simply a subset of the scaling functions) to splines of higher degree. We then use the lifting scheme in order to improve the approximation properties with respect to a norm induced by a weighted inner product with a piecewise constant weight function. Using the lifted wavelets we define a multiresolution analysis of tensor-product spline functions and apply it to image compression of black-and-white images. By performing-as a model problem-image compression with black-and-white images, we demonstrate that the use of a weight function allows to adapt the norm to the specific problem. 相似文献
16.
Often, the Dyadic Wavelet Transform is performed and implemented with the Daubechies wavelets, the Battle-Lemarie wavelets,
or the splines wavelets, whereas in continuous-time wavelet decomposition a much larger variety of mother wavelets is used.
Maintaining the dyadic time-frequency sampling and the recursive pyramidal computational structure, we present various methods
for constructing wavelets ψwanted, with some desired shape and properties and which are
associated with semi-orthogonal multiresolution analyses. We explain in detail how to design any desired wavelet, starting
from any given multiresolution analysis. We also explicitly derive the formulae of the filter bank structure that implements
the designed wavelet. We illustrate these wavelet design techniques with examples that we have programmed with Matlab routines. 相似文献
17.
A multiresolution analysis of a curve is normal if
each wavelet detail vector with respect to a certain subdivision
scheme lies in the local normal direction. In this paper we study
properties such as regularity, convergence, and stability of a
normal multiresolution analysis. In particular, we show that these
properties critically depend on the underlying subdivision scheme
and that, in general, the convergence of normal multiresolution
approximations equals the convergence of the underlying subdivision
scheme. 相似文献
18.
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20.
Jianzhong Wang 《Journal of Computational Analysis and Applications》2003,5(1):179-193
In many applications, the splines on an arbitrary partition are very useful. In this paper, a spline wavelet structure is created in the way that it provides a multiresolution approximation of the spline subspaces with arbitrary partition in the space of continuous functions on a finite interval. Based on the wavelet basis and the wavelet packet in this structure, a multi-level interpolation method is developed for decomposing a function into wavelet series and reconstructing it from its wavelet representation. 相似文献