In this paper, supose Γ be a boundary of a Jordan domain D and Γ satisfied Альпер condition, the order that rational type interpolating operators at Fejer's points of f(z)∈C(Γ) converge to f(z) in the se...In this paper, supose Γ be a boundary of a Jordan domain D and Γ satisfied Альпер condition, the order that rational type interpolating operators at Fejer's points of f(z)∈C(Γ) converge to f(z) in the sense of uniformly convergence is obtained.展开更多
The paper gives a new way of constructing Hermite Fejer and Hermite interpolatory polynomials with the nodes of the roots of first kind of Chebyshev polynomials and gives the approximation order of these two kinds of...The paper gives a new way of constructing Hermite Fejer and Hermite interpolatory polynomials with the nodes of the roots of first kind of Chebyshev polynomials and gives the approximation order of these two kinds of operators. The approximation orders are described with the best rate of approximation of f by polynomials of degree N=(q+1)n 1 in L p w spaces.展开更多
The relationship between the order of approximation by neural network based on scattered threshold value nodes and the neurons involved in a single hidden layer is investigated. The results obtained show that the degr...The relationship between the order of approximation by neural network based on scattered threshold value nodes and the neurons involved in a single hidden layer is investigated. The results obtained show that the degree of approximation by the periodic neural network with one hidden layer and scattered threshold value nodes is increased with the increase of the number of neurons hid in hidden layer and the smoothness of excitation function.展开更多
In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,w...In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,we also get some other results about the mean approximation.展开更多
In this paper we introduce the two-parameter operators on Abelian group and establish their interpolation theorems of approximation, which are extensions of the interpolation theorems for nonlinear best approximation ...In this paper we introduce the two-parameter operators on Abelian group and establish their interpolation theorems of approximation, which are extensions of the interpolation theorems for nonlinear best approximation by R. Devore and are suitable for the approximation of oprators.展开更多
The state space average model of switching converters transforms time varying differential equations into time invariant differential equations by the averaging method in math.The model has merits of simple,clear phys...The state space average model of switching converters transforms time varying differential equations into time invariant differential equations by the averaging method in math.The model has merits of simple,clear physical conception and easy to design control system,but it exhibits significant steadystate error and delayed dynamic response in some special parameters or state conditions.Besides,the conventional state space average model(CSSAM)can’t reflect how much the switching period influences system performance.The averaging method based on exact time domain solution approximation for the state variable is established in this paper.Subsequently,a second-order state-space average model(SOSSAM)which extends the constant term in CSSAM to a combination of constant term and linear term of the switching period is proposed.This model inherits the advantages of CSSAM and improves accuracy of steady state performance and dynamic response of switching converters.Influence of switching period to system performance is reflected,which lays a foundation for analyzing system performance and designing a control system of switching converters.展开更多
Generalized Bernstein-Kantorovich polynomials M_n^((k))(a_n, f, x) were introduced in the paper and their order of approximation were estimated in the L_p[0, 1]-spaces.
In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on comp...In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.展开更多
In this paper, by means of combining non-probabilistic convex modeling with perturbation theory, an improvement is made on the first order approximate solution in convex models of uncertainties. Convex modeling is ext...In this paper, by means of combining non-probabilistic convex modeling with perturbation theory, an improvement is made on the first order approximate solution in convex models of uncertainties. Convex modeling is extended to largely uncertain and non-convex sets of uncertainties and the combinational convex modeling is developed. The presented method not only extends applications of convex modeling, but also improves its accuracy in uncertain problems and computational efficiency. The numerical example illustrates the efficiency of the proposed method.展开更多
When approximation order is an odd positive integer, a simple method is given to construct compactly supported orthogonal symmetric complex scaling function with dilation factor 3. Two corresponding orthogonal wavelet...When approximation order is an odd positive integer, a simple method is given to construct compactly supported orthogonal symmetric complex scaling function with dilation factor 3. Two corresponding orthogonal wavelets, one is symmetric and the other is antisymmetric about origin, are constructed explicitly. Additionally, when approximation order is an even integer 2, we also give a method to construct compactly supported orthogonal symmetric complex that illustrate the corresponding results. wavelets. In the end, there are several examples展开更多
In this paper, an interpolation polynomial operator F n(f; l,x) is constructed based on the zeros of a kind of Jacobi polynomials as the interpolation nodes. For any continuous function f(x)∈C b [-1,1] ...In this paper, an interpolation polynomial operator F n(f; l,x) is constructed based on the zeros of a kind of Jacobi polynomials as the interpolation nodes. For any continuous function f(x)∈C b [-1,1] (0≤b≤l) F n(f; l,x) converges to f(x) uniformly, where l is an odd number.展开更多
Based on a node group <img src="Edit_effba4ca-e855-418a-8a72-d70cb1ec3470.png" width="240" height="46" alt="" />, the Newman type rational operator is constructed in the p...Based on a node group <img src="Edit_effba4ca-e855-418a-8a72-d70cb1ec3470.png" width="240" height="46" alt="" />, the Newman type rational operator is constructed in the paper. The convergence rate of approximation to a class of non-smooth functions is discussed, which is <img src="Edit_174e8f70-651b-4abb-a8f3-a16a576536dc.png" width="85" height="50" alt="" /> regarding to X. Moreover, if the operator is constructed based on further subdivision nodes, the convergence rate is <img src="Edit_557b3a01-7f56-41c0-bb67-deab88b9cc63.png" width="85" height="45" alt="" />. The result in this paper is superior to the approximation results based on equidistant nodes, Chebyshev nodes of the first kind and Chebyshev nodes of the second kind.展开更多
The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this arti...The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this article. Furthermore, the stability of convergence of Tn,∈（f,z） with disturbed sample values f（z^＊） ＋ Sk are also proved in this article.展开更多
ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB...ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB-spline curves of arbitrary order ofωB-spline curves and prove its C^k?2-continuity by two kinds of methods.The first method directly prove that the sequence of control polygons of subdivision of order k converges to a C^k?2-continuousωB-spline curve of order k.The second one is based on the theories upon subdivision masks and asymptotic equivalence etc.,which is more convenient to be further extended to the case of surface subdivision.And the problem of approximation order of this non-stationary subdivision scheme is also discussed.Then a uniform ωB-spline curve has both perfect mathematical representation and efficient generation method,which will benefit the application ofωB-splines.展开更多
The discrete scalar data need prefiltering when transformed by discrete multi-wavelet, but prefiltering will make some properties of multi-wavelets lost. Balanced multi-wavelets can avoid prefiltering. The sufficient ...The discrete scalar data need prefiltering when transformed by discrete multi-wavelet, but prefiltering will make some properties of multi-wavelets lost. Balanced multi-wavelets can avoid prefiltering. The sufficient and necessary condition of p-order balance for multi-wavelets in time domain, the interrelation between balance order and approximation order and the sampling property of balanced multi-wavelets are investigated. The algorithms of 1-order and 2-order balancing for multi-wavelets are obtained. The two algorithms both preserve the orthogonal relation between multi-scaling function and multi-wavelets. More importantly, balancing operation doesnt increase the length of filters, which suggests that a relatively short balanced multi-wavelet can be constructed from an existing unbalanced multi-wavelet as short as possible.展开更多
The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.
This paper discover that when disturbance occurs on Chebyshev knot, so long as the disturbance amount does not exceed , then the course of the quasi Hemite-Fejer interpolation on the disturbed Chebyshev knot still ke...This paper discover that when disturbance occurs on Chebyshev knot, so long as the disturbance amount does not exceed , then the course of the quasi Hemite-Fejer interpolation on the disturbed Chebyshev knot still keeps the converge uniformly properlies for any continuous function on . Besides,the paper estimates the convergance rate.展开更多
In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new ...In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new insertion control points on a finer grid are computed by weighted sums of already existing control points. In the limit of the recursive process, data is defined on a dense set of point, The objective is to find an improved subdivision approximating algorithm which has a smaller support and a higher approximating order. The author chooses a ternary scheme because the best way to get a smaller support is to pass from the binary to ternary or complex algorithm and uses polynomial reproducing propriety to get higher approximation order. Using the cardinal Lagrange polynomials the author has proposed a 4-point approximating ternary subdivision algorithm and found that a higher regularity of limit function does not guarantee a higher approximating order. The proposed 4-point ternary approximation subdivision family algorithms with the mask a have the limit function in C2 and have approximation order 4. Also the author has demonstrated that in this class there is no algorithm whose limit function is in C3. It can be seen that this stationary ternary 4-point approximating symmetrical subdivision algorithm has a lower computational cost than the 6-point binary approximation subdivision algorithm for a greater range of points.展开更多
文摘In this paper, supose Γ be a boundary of a Jordan domain D and Γ satisfied Альпер condition, the order that rational type interpolating operators at Fejer's points of f(z)∈C(Γ) converge to f(z) in the sense of uniformly convergence is obtained.
文摘The paper gives a new way of constructing Hermite Fejer and Hermite interpolatory polynomials with the nodes of the roots of first kind of Chebyshev polynomials and gives the approximation order of these two kinds of operators. The approximation orders are described with the best rate of approximation of f by polynomials of degree N=(q+1)n 1 in L p w spaces.
文摘The relationship between the order of approximation by neural network based on scattered threshold value nodes and the neurons involved in a single hidden layer is investigated. The results obtained show that the degree of approximation by the periodic neural network with one hidden layer and scattered threshold value nodes is increased with the increase of the number of neurons hid in hidden layer and the smoothness of excitation function.
文摘In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,we also get some other results about the mean approximation.
文摘In this paper we introduce the two-parameter operators on Abelian group and establish their interpolation theorems of approximation, which are extensions of the interpolation theorems for nonlinear best approximation by R. Devore and are suitable for the approximation of oprators.
基金supported by National Natural Science Foundation of China(518707211).
文摘The state space average model of switching converters transforms time varying differential equations into time invariant differential equations by the averaging method in math.The model has merits of simple,clear physical conception and easy to design control system,but it exhibits significant steadystate error and delayed dynamic response in some special parameters or state conditions.Besides,the conventional state space average model(CSSAM)can’t reflect how much the switching period influences system performance.The averaging method based on exact time domain solution approximation for the state variable is established in this paper.Subsequently,a second-order state-space average model(SOSSAM)which extends the constant term in CSSAM to a combination of constant term and linear term of the switching period is proposed.This model inherits the advantages of CSSAM and improves accuracy of steady state performance and dynamic response of switching converters.Influence of switching period to system performance is reflected,which lays a foundation for analyzing system performance and designing a control system of switching converters.
文摘Generalized Bernstein-Kantorovich polynomials M_n^((k))(a_n, f, x) were introduced in the paper and their order of approximation were estimated in the L_p[0, 1]-spaces.
文摘In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.
基金The project supported by the National Outstanding Youth Science Foundation of China the National Post Doctor Science Foundation of China
文摘In this paper, by means of combining non-probabilistic convex modeling with perturbation theory, an improvement is made on the first order approximate solution in convex models of uncertainties. Convex modeling is extended to largely uncertain and non-convex sets of uncertainties and the combinational convex modeling is developed. The presented method not only extends applications of convex modeling, but also improves its accuracy in uncertain problems and computational efficiency. The numerical example illustrates the efficiency of the proposed method.
基金supported by the National Natural Science Foundation of China (11071152, 11126343)the Natural Science Foundation of Guangdong Province(10151503101000025, S2011010004511)
文摘When approximation order is an odd positive integer, a simple method is given to construct compactly supported orthogonal symmetric complex scaling function with dilation factor 3. Two corresponding orthogonal wavelets, one is symmetric and the other is antisymmetric about origin, are constructed explicitly. Additionally, when approximation order is an even integer 2, we also give a method to construct compactly supported orthogonal symmetric complex that illustrate the corresponding results. wavelets. In the end, there are several examples
文摘In this paper, an interpolation polynomial operator F n(f; l,x) is constructed based on the zeros of a kind of Jacobi polynomials as the interpolation nodes. For any continuous function f(x)∈C b [-1,1] (0≤b≤l) F n(f; l,x) converges to f(x) uniformly, where l is an odd number.
文摘Based on a node group <img src="Edit_effba4ca-e855-418a-8a72-d70cb1ec3470.png" width="240" height="46" alt="" />, the Newman type rational operator is constructed in the paper. The convergence rate of approximation to a class of non-smooth functions is discussed, which is <img src="Edit_174e8f70-651b-4abb-a8f3-a16a576536dc.png" width="85" height="50" alt="" /> regarding to X. Moreover, if the operator is constructed based on further subdivision nodes, the convergence rate is <img src="Edit_557b3a01-7f56-41c0-bb67-deab88b9cc63.png" width="85" height="45" alt="" />. The result in this paper is superior to the approximation results based on equidistant nodes, Chebyshev nodes of the first kind and Chebyshev nodes of the second kind.
基金Supported by NSF of Henan Province of China(20001110001)
文摘The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this article. Furthermore, the stability of convergence of Tn,∈（f,z） with disturbed sample values f（z^＊） ＋ Sk are also proved in this article.
基金the National Natural Science Foundation of China(61772164,61761136010)the Natural Science Foundation of Zhejiang Province(LY17F020025).
文摘ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB-spline curves of arbitrary order ofωB-spline curves and prove its C^k?2-continuity by two kinds of methods.The first method directly prove that the sequence of control polygons of subdivision of order k converges to a C^k?2-continuousωB-spline curve of order k.The second one is based on the theories upon subdivision masks and asymptotic equivalence etc.,which is more convenient to be further extended to the case of surface subdivision.And the problem of approximation order of this non-stationary subdivision scheme is also discussed.Then a uniform ωB-spline curve has both perfect mathematical representation and efficient generation method,which will benefit the application ofωB-splines.
基金Supported by the Scientific Research Foundation for Returned Overseas Chinese Scholars from the State Education Ministry (No. [2002]247) and the Young Key Teachers Foundation of Chongqing University.
文摘The discrete scalar data need prefiltering when transformed by discrete multi-wavelet, but prefiltering will make some properties of multi-wavelets lost. Balanced multi-wavelets can avoid prefiltering. The sufficient and necessary condition of p-order balance for multi-wavelets in time domain, the interrelation between balance order and approximation order and the sampling property of balanced multi-wavelets are investigated. The algorithms of 1-order and 2-order balancing for multi-wavelets are obtained. The two algorithms both preserve the orthogonal relation between multi-scaling function and multi-wavelets. More importantly, balancing operation doesnt increase the length of filters, which suggests that a relatively short balanced multi-wavelet can be constructed from an existing unbalanced multi-wavelet as short as possible.
基金Supported by the Natural Science Foundation of the Education Department of Henan Province(2006110001)Supported by the Natural Science Foundation of Henan University of China (XK03YBSX002)
文摘The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.
文摘This paper discover that when disturbance occurs on Chebyshev knot, so long as the disturbance amount does not exceed , then the course of the quasi Hemite-Fejer interpolation on the disturbed Chebyshev knot still keeps the converge uniformly properlies for any continuous function on . Besides,the paper estimates the convergance rate.
文摘In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new insertion control points on a finer grid are computed by weighted sums of already existing control points. In the limit of the recursive process, data is defined on a dense set of point, The objective is to find an improved subdivision approximating algorithm which has a smaller support and a higher approximating order. The author chooses a ternary scheme because the best way to get a smaller support is to pass from the binary to ternary or complex algorithm and uses polynomial reproducing propriety to get higher approximation order. Using the cardinal Lagrange polynomials the author has proposed a 4-point approximating ternary subdivision algorithm and found that a higher regularity of limit function does not guarantee a higher approximating order. The proposed 4-point ternary approximation subdivision family algorithms with the mask a have the limit function in C2 and have approximation order 4. Also the author has demonstrated that in this class there is no algorithm whose limit function is in C3. It can be seen that this stationary ternary 4-point approximating symmetrical subdivision algorithm has a lower computational cost than the 6-point binary approximation subdivision algorithm for a greater range of points.
