We construct a tree wavelet approximation by using a constructive greedy scheme(CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a presc...We construct a tree wavelet approximation by using a constructive greedy scheme(CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.展开更多
Let otherwise and F(x,y).be a continuous distribution function on R^2. Then there exist linear wavelet operators L_n(F,x,y)which are also distribution function and where the defining them mother wavelet is(x,y).These ...Let otherwise and F(x,y).be a continuous distribution function on R^2. Then there exist linear wavelet operators L_n(F,x,y)which are also distribution function and where the defining them mother wavelet is(x,y).These approximate F(x,y)in the supnorm.The degree of this approximation is estimated by establishing a Jackson type inequality.Furthermore we give generalizations for the case of a mother wavelet ≠,which is just any distribution function on R^2,also we extend these results in R^r,r>2.展开更多
In this paper we estimate the degree of approximation of wavelet expansions. Our result shows that the degree has the exponential decay for function f(x)∈L2 continuous in a finite interval (a, b) which is much superi...In this paper we estimate the degree of approximation of wavelet expansions. Our result shows that the degree has the exponential decay for function f(x)∈L2 continuous in a finite interval (a, b) which is much superior to those of approximation by polynomial operators and by expansions of classical orthogonal series.展开更多
The existence of approximate inertial manifold Using wavelet to Burgers' equation, and numerical solution under multiresolution analysis with the low modes were studied. It is shown that the Burgers' equation ...The existence of approximate inertial manifold Using wavelet to Burgers' equation, and numerical solution under multiresolution analysis with the low modes were studied. It is shown that the Burgers' equation has a good localization property of the numerical solution distinguishably.展开更多
In this paper, we present a numerical method for solving two-dimensional VolterraFredholm integral equations of the second kind（2DV-FK2）. Our method is based on approximating unknown function with Bernstein polynomi...In this paper, we present a numerical method for solving two-dimensional VolterraFredholm integral equations of the second kind（2DV-FK2）. Our method is based on approximating unknown function with Bernstein polynomials. We obtain an error bound for this method and employ the method on some numerical tests to show the efficiency of the method.展开更多
Subdivision algorithm （Stationary or Non-stationary） is one of the most active and exciting research topics in wavelet analysis and applied mathematical theory. In multidimensional non-stationary situation, its limi...Subdivision algorithm （Stationary or Non-stationary） is one of the most active and exciting research topics in wavelet analysis and applied mathematical theory. In multidimensional non-stationary situation, its limit functions are both compactly supported and infinitely differentiable. Also, these limit functions can serve as the scaling functions to generate the multidimensional non-stationary orthogonal or biorthogonal semi-multiresolution analysis （Semi-MRAs）. The spectral approximation property of multidimensional non-stationary biorthogonal Semi-MRAs is considered in this paper. Based on nonstationary subdivision scheme and its limit scaling functions, it is shown that the multidimensional nonstationary biorthogonal Semi-MRAs have spectral approximation order r in Sobolev space H^s（R^d）, for all r ≥ s ≥ 0.展开更多
基金This work was supported in part by the US National Science Foundation under grant DMS-9973427 and CCR-0312113by NASA under grant NCC5-399+1 种基金by Natural Science Foundation of China under grant 10371122by the Chinese Academy of Sciences under the program of"One Hundred Distinguished Young Scientists".
文摘We construct a tree wavelet approximation by using a constructive greedy scheme(CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.
文摘Let otherwise and F(x,y).be a continuous distribution function on R^2. Then there exist linear wavelet operators L_n(F,x,y)which are also distribution function and where the defining them mother wavelet is(x,y).These approximate F(x,y)in the supnorm.The degree of this approximation is estimated by establishing a Jackson type inequality.Furthermore we give generalizations for the case of a mother wavelet ≠,which is just any distribution function on R^2,also we extend these results in R^r,r>2.
基金This work is supported by the Natural Science Foundation of Zhejiang,PR China.
文摘In this paper we estimate the degree of approximation of wavelet expansions. Our result shows that the degree has the exponential decay for function f(x)∈L2 continuous in a finite interval (a, b) which is much superior to those of approximation by polynomial operators and by expansions of classical orthogonal series.
文摘The existence of approximate inertial manifold Using wavelet to Burgers' equation, and numerical solution under multiresolution analysis with the low modes were studied. It is shown that the Burgers' equation has a good localization property of the numerical solution distinguishably.
基金Supported by the Center of Excellence for Mathematics,Shahrekord University,Iran
文摘In this paper, we present a numerical method for solving two-dimensional VolterraFredholm integral equations of the second kind（2DV-FK2）. Our method is based on approximating unknown function with Bernstein polynomials. We obtain an error bound for this method and employ the method on some numerical tests to show the efficiency of the method.
文摘Subdivision algorithm （Stationary or Non-stationary） is one of the most active and exciting research topics in wavelet analysis and applied mathematical theory. In multidimensional non-stationary situation, its limit functions are both compactly supported and infinitely differentiable. Also, these limit functions can serve as the scaling functions to generate the multidimensional non-stationary orthogonal or biorthogonal semi-multiresolution analysis （Semi-MRAs）. The spectral approximation property of multidimensional non-stationary biorthogonal Semi-MRAs is considered in this paper. Based on nonstationary subdivision scheme and its limit scaling functions, it is shown that the multidimensional nonstationary biorthogonal Semi-MRAs have spectral approximation order r in Sobolev space H^s（R^d）, for all r ≥ s ≥ 0.
