共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we introduce complex pseudo splines that are derived from pseudo splines of type I. First, we show that the
shifts of every complex pseudo spline are linearly independent. Therefore we can construct a biorthogonal wavelet system.
Next, we investigate the Riesz basis property of the corresponding wavelet system generated by complex pseudo splines. The
regularity of the complex pseudo splines will be analyzed. Furthermore, by using complex pseudo splines, we will construct
symmetric or antisymmetric complex tight framelets with desired approximation order. 相似文献
2.
3.
We study biorthogonal bases of compactly supported wavelets constructed from box splines in ℝ
N
with any integer dilation factor. For a suitable class of box splines we write explicitly dual low-pass filters of arbitrarily
high regularity and indicate how to construct the corresponding high-pass filters (primal and dual).
Received: August 23, 2000; in final form: March 10, 2001?Published online: May 29, 2002 相似文献
4.
Valery A. Zheludev 《分析论及其应用》1998,14(4):66-88
In this paper we consider polynomial splines S(x) with equidistant nodes which may grow as O (|x|s). We present an integral representation of such splines with a distribution kernel. This representation is related to the
Fourier integral of slowly growing functions. The part of the Fourier exponentials herewith play the so called exponential
splines by Schoenberg. The integral representation provides a flexible tool for dealing with the growing equidistant splines.
First, it allows us to construct a rich library of splines possessing the property that translations of any such spline form
a basis of corresponding spline space. It is shown that any such spline is associated with a dual spline whose translations
form a biorthogonal basis. As examples we present solutions of the problems of projection of a growing function onto spline
spaces and of spline interpolation of a growing function. We derive formulas for approximate evaluation of splines projecting
a function onto the spline space and establish therewith exact estimations of the approximation errors. 相似文献
5.
6.
一对拟双正交框架小波 总被引:1,自引:0,他引:1
对于一对对偶框架多尺度分析,借助于滤波器,我们构造一对对偶框架小波和一对拟双正交框架小波,并且指出一对对偶框架小波和一对拟双正交框架小波的滤波器所满足的充分必要条件. 相似文献
7.
Borislav Bojanov 《Numerische Mathematik》1993,65(1):63-75
Summary We give a complete characterization of the Hermite interpolation problem by periodic splines with Birkhoff knots. As a dual result we derive the characterization of the Birkhoff interpolation by periodic splines with multiple knots.Sponsored by the Bulgarian Ministry of Education and Science under Contract No. MM-15 相似文献
8.
Interproximation methods for surfaces can be used to construct a smooth surface interpolating some data points and passing through specified regions. In this paper we study the use of mixed splines, that is smoothing splines with additional interpolation constraints, to solve the interproximation problem for surfaces in the case of scattered data. The solution is obtained by solving a linear system whose structure can be improved by using “bell-shaped” thin plate splines. 相似文献
9.
Phillip J. Barry Ronald N. Goldman Charles A. Micchelli 《Advances in Computational Mathematics》1993,1(2):139-171
We show that many fundamental algorithms and techniques for B-spline curves extend to geometrically continuous splines. The algorithms, which are all related to knot insertion, include recursive evaluation, differentiation, and change of basis. While the algorithms for geometrically continuous splines are not as computationally simple as those for B-spline curves, they share the same general structure. The techniques we investigate include knot insertion, dual functionals, and polar forms; these prove to be useful theoretical tools for studying geometrically continuous splines. 相似文献
10.
Hossein Behforooz 《Applied mathematics and computation》2010,216(2):364-367
Recently, Behforooz [1], has introduced a new approach to construct cubic splines by using the integral values, rather than the usual function values at the knots. Also he has established different sets of end conditions for cubic and quintic splines by using the integral values, see Behforooz [2], [3] and [4]. In this paper, we will use the same techniques of [1] to construct integro quintic splines. Although by using the integral values we expected to face a more complicated process for our construction, it turned out that the matrix of the system of linear equations that produces the parameters became a diagonally dominant matrix and the process became very simple. The selection of the required end conditions for our integro quintic splines will be discussed. The numerical examples and computational results illustrate and guarantee a higher accuracy for this approximation. 相似文献
11.
We construct new non-separable splines and we apply the spline sampling approximation to the computation of numerical solutions of evolution equations. The non-separable splines are basis functions which give a fine sampling approximation which enables us to compute numerical solutions by means of the method of lines combined with the Galerkin method. To demonstrate our approach we compute numerical solutions of the Burgers equation and the Kadomtsev–Petviashvili equation. 相似文献
12.
利用Wilson的方法,可构造出一函数族,本文得到它们成为标架的判定条件.此外,还得到了其对偶标架的性质. 相似文献
13.
In this paper, we exploit the relation between the regularity of refinable functions with non-integer dilations and the distribution
of powers of a fixed number modulo 1, and show the nonexistence of a non-trivial C
∞ solution of the refinement equation with non-integer dilations. Using this, we extend the results on the refinable splines
with non-integer dilations and construct a counterexample to some conjecture concerning the refinable splines with non-integer
dilations. Finally, we study the box splines satisfying the refinement equation with non-integer dilation and translations.
Our study involves techniques from number theory and harmonic analysis. 相似文献
14.
15.
In this work, the relationship between splines and the linear control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations. 相似文献
16.
Starting from any two compactly supported refinable functions in L2(R)
with dilation factor d,we show that it is always possible to construct 2d wavelet functions
with compact support such that they generate a pair of dual d-wavelet frames in L2(R).
Moreover, the number of vanishing moments of each of these wavelet frames is equal
to the approximation order of the dual MRA; this is the highest possible. In particular,
when we consider symmetric refinable functions, the constructed dual wavelets are also
symmetric or antisymmetric. As a consequence, for any compactly supported refinable
function in L2(R), it is possible to construct, explicitly and easily, wavelets that are
finite linear combinations of translates (d · – k), and that generate a wavelet frame with
an arbitrarily preassigned number of vanishing moments.We illustrate the general theory
by examples of such pairs of dual wavelet frames derived from B-spline functions. 相似文献
17.
In this paper, starting from any two functions satisfying some simple conditions, using a periodization method, we construct a dual pair of periodic wavelet frames and show their optimal bounds. The obtained periodic wavelet frames possess trigonometric polynomial expressions. Finally, we present two examples to explain our theory. 相似文献
18.
Yu. N. Subbotin 《Proceedings of the Steklov Institute of Mathematics》2007,259(2):S231-S242
In this paper with the help of parabolic splines we construct a linear method of approximate recovery of functions by their values on an arbitrary grid. In the method, a spline inherits the properties of monotonicity and convexity from the approximated function, and is sufficiently smooth. In addition, the constructed linear operator as an operator acting from the space of continuous functions to the same space has the norm equal to one. We also obtain similar results for trigonometric splines of third order. 相似文献
19.
Sara Remogna 《Advances in Computational Mathematics》2012,36(1):39-65
In this paper we construct discrete quasi-interpolants based on C
2 cubic multi-box splines on uniform Powell–Sabin triangulations of a rectangular domain. The main problem consists in finding
the coefficient functionals associated with boundary multi-box splines (i.e. multi-box splines whose supports overlap with
the domain) involving data points inside or on the boundary of the domain and giving the optimal approximation order. They
are obtained either by minimizing an upper bound for the infinity norm of the operator w.r.t. a finite number of free parameters,
or by inducing the superconvergence of the gradient of the quasi-interpolant at some specific points of the domain. Finally,
we give norm and error estimates and we provide some numerical examples illustrating the approximation properties of the proposed
operators. 相似文献
20.
Ming-Jun Lai 《Numerical Algorithms》1992,2(1):33-38
We describe an algorithm to compute the B-nets of bivariate box splines on a three-or four-directional mesh. Two pseudo Fortran programs for those B-nets are given.Research supported by a Faculty Grant From the University of Utah Research Committee. 相似文献