Biorthogonal Spline Wavelets on the Interval
نویسنده
چکیده
We investigate biorthogonal spline wavelets on the interval. We give sufficient and necessary conditions for the reconstruction and decomposition matrices to be sparse. Furthermore, we give numerical estimates for the Riesz stability of such bases. §
منابع مشابه
Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems
In this paper, a new numerical method for solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon biorthogonal cubic Hermite spline multiwavelets approximations. The properties of biorthogonal multiwavelets are first given. The operational matrix of fractional Riemann-Lioville in...
متن کاملA new view on biorthogonal spline wavelets
The biorthogonal wavelets introduced by Cohen, Daubechies, and Feauveau contain in particular compactly supported biorthogonal spline wavelets with compactly supported duals. We present a new approach for the construction of compactly supported spline wavelets, which is entirely based on properties of splines in the time domain. We are able to characterize a large class of such wavelets which c...
متن کاملConstruction of compactly supported biorthogonal wavelets
This paper presents a construction of compactly supported biorthogonal spline wavelets in L2(IR ). In particular, a concrete method for the construction of bivariate compactly supported biorthogonal wavelets from box splines of increasing smoothness is provided. Several examples are given to illustrate the method. Key-Words:multivariate biorthogonal wavelets, multivariate wavelets, box splines,...
متن کاملThe Wavelet Element Method Part II: Realization and Additional Features in 2D and 3D
The Wavelet Element Method (WEM) provides a construction of multiresolution systems and biorthogonal wavelets on fairly general domains. These are split into subdomains that are mapped to a single reference hypercube. Tensor products of scaling functions and wavelets defined on the unit interval are used on the reference domain. By introducing appropriate matching conditions across the interele...
متن کاملBiorthogonal Spline-Wavelets on the Interval | Stability and Moment Conditions
This paper is concerned with the construction of biorthogonal multiresolution analyses on [0; 1] such that the corresponding wavelets realize any desired order of moment conditions throughout the interval. Our starting point is the family of biorthogonal pairs consisting of cardinal B-splines and compactly supported dual generators on IR developed by Cohen, Daubechies and Feauveau. In contrast ...
متن کامل