The paper proves that, if f（x） ∈ L^p[-1,1],1≤p〈∞ ,changes sign I times in （-1, 1）,then there exists a real rational function r（x） ∈ Rn^（2μ-1）l which is eopositive with f（x）, such that the following Ja...The paper proves that, if f（x） ∈ L^p[-1,1],1≤p〈∞ ,changes sign I times in （-1, 1）,then there exists a real rational function r（x） ∈ Rn^（2μ-1）l which is eopositive with f（x）, such that the following Jackson type estimate ｜｜f-r｜｜p≤Cδl^2μωφ（f,1/n）p holds, where μ is a natural number ≥3/2＋1/p, and Cδ is a positive constant depending only on δ.展开更多
In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches ...In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches zero.展开更多
Let Γ be a regular curve and Lp (Γ), 1<p<+∞. be the class of all complex - valued functions f de-fined on Γ which are such that |f|p is mtegrabie in sense of Lebesgue. In this work, we define the k th p-Fabc...Let Γ be a regular curve and Lp (Γ), 1<p<+∞. be the class of all complex - valued functions f de-fined on Γ which are such that |f|p is mtegrabie in sense of Lebesgue. In this work, we define the k th p-Fabcrpolynomial F k,p (z),the kth p-Faber principle part F k.p (1/z) for Γ , and defined the nth p-Fcber- Laurent rational function Rn.p (f, z) and p- generalized modulus of continuity Ωp(f, t) of a function f of Lp(Γ) We inves-tigate some properties of Fk,p (z) and Fk.p (1/z). And then we prove a direct theorem characterizing the degree of approximation with respect to Ω (. , t) in the mean of functions of Lp(Γ) by the rational junctions Rn.p (. . z).展开更多
Let f be a function, continuous and real valued on the segment △,△ (-∞,∞) and {Rn} be the sequence of the rational functions of best uniform approximation to fon △ of order (n,n). In the present work, the converg...Let f be a function, continuous and real valued on the segment △,△ (-∞,∞) and {Rn} be the sequence of the rational functions of best uniform approximation to fon △ of order (n,n). In the present work, the convergence of {Rn} in the complex plane is considered for the special caseswhen the poles (or the zeros, respectively) of {Rn} accumulate in the terms of weak convergence of measures to acompact set of zera capacity.As a consequence, sufficient conditions for the holomorphic and the meromorphic continuability of fare given.展开更多
Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of th...Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.展开更多
In this paper, we research the Miintz rational approximation of two kinds of spe- cial function classes, and give the corresponding estimates of approximation rates of these classes.
This paper presents an adaptive rationalized Haar function approximation method to obtain the optimal injection strategy for alkali-surfactant-polymer(ASP) flooding. In this process, the non-uniform control vector par...This paper presents an adaptive rationalized Haar function approximation method to obtain the optimal injection strategy for alkali-surfactant-polymer(ASP) flooding. In this process, the non-uniform control vector parameterization is introduced to convert original problem into a multistage optimization problem, in which a new normalized time variable is adopted on the combination of the subinterval length. Then the rationalized Haar function approximation method, in which an auxiliary function is introduced to dispose path constraints, is used to transform the multistage problem into a nonlinear programming. Furthermore, an adaptive strategy proposed on the basis of errors is adopted to regulate the order of Haar function vectors. Finally, the nonlinear programming for ASP flooding is solved by sequential quadratic programming. To illustrate the performance of proposed method,the experimental comparison method and control vector parameterization(CVP) method are introduced to optimize the original problem directly. By contrastive analysis of results, the accuracy and efficiency of proposed method are confirmed.展开更多
Recently we have reported a new method of rational approximation of the sinc function obtained by sampling and the Fourier transforms. However, this method requires a trigonometric multiplier that originates from the ...Recently we have reported a new method of rational approximation of the sinc function obtained by sampling and the Fourier transforms. However, this method requires a trigonometric multiplier that originates from the shifting property of the Fourier transform. In this work, we show how to represent the Fourier transform of a function <em>f</em>(<em>t</em>) in form of a ratio of two polynomials without any trigonometric multiplier. A MATLAB code showing algorithmic implementation of the proposed method for rational approximation of the Fourier transform is presented.展开更多
In the present note,we consider the problem:how many interpolation nodes can be deleted from the Newman-type rational function such that the convergence rate still achieve.
Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed： one uses the contour integral representation and conformal real〉 ping, and the other is based on a version of the mu...Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed： one uses the contour integral representation and conformal real〉 ping, and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic structure calculations.展开更多
基金supported by the National Natural Science Foundation of China (10901044)Research Project of Hangzhou Normal University (YS05203154)
文摘The paper proves that, if f（x） ∈ L^p[-1,1],1≤p〈∞ ,changes sign I times in （-1, 1）,then there exists a real rational function r（x） ∈ Rn^（2μ-1）l which is eopositive with f（x）, such that the following Jackson type estimate ｜｜f-r｜｜p≤Cδl^2μωφ（f,1/n）p holds, where μ is a natural number ≥3/2＋1/p, and Cδ is a positive constant depending only on δ.
基金This research is suported by National Science foundation Grant.
文摘In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches zero.
文摘Let Γ be a regular curve and Lp (Γ), 1<p<+∞. be the class of all complex - valued functions f de-fined on Γ which are such that |f|p is mtegrabie in sense of Lebesgue. In this work, we define the k th p-Fabcrpolynomial F k,p (z),the kth p-Faber principle part F k.p (1/z) for Γ , and defined the nth p-Fcber- Laurent rational function Rn.p (f, z) and p- generalized modulus of continuity Ωp(f, t) of a function f of Lp(Γ) We inves-tigate some properties of Fk,p (z) and Fk.p (1/z). And then we prove a direct theorem characterizing the degree of approximation with respect to Ω (. , t) in the mean of functions of Lp(Γ) by the rational junctions Rn.p (. . z).
基金The work is supported by Project 69 with Ministry of ScienceEducation, Bulgaria.
文摘Let f be a function, continuous and real valued on the segment △,△ (-∞,∞) and {Rn} be the sequence of the rational functions of best uniform approximation to fon △ of order (n,n). In the present work, the convergence of {Rn} in the complex plane is considered for the special caseswhen the poles (or the zeros, respectively) of {Rn} accumulate in the terms of weak convergence of measures to acompact set of zera capacity.As a consequence, sufficient conditions for the holomorphic and the meromorphic continuability of fare given.
基金supported by the National Science Foundation of China(No.11161033)Inner Mongolia Normal University Talent Project Foundation(No.RCPY-2-2012-K-036)
文摘Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.
基金Supported by the National Natural Science Foundation of China(11161033)Inner Mongolia Natural Science Foundation (2009MS0105)
文摘In this paper, we research the Miintz rational approximation of two kinds of spe- cial function classes, and give the corresponding estimates of approximation rates of these classes.
基金Supported by the National Natural Science Foundation of China(61573378)the Fundamental Research Funds for the Central Universities(15CX06064A)
文摘This paper presents an adaptive rationalized Haar function approximation method to obtain the optimal injection strategy for alkali-surfactant-polymer(ASP) flooding. In this process, the non-uniform control vector parameterization is introduced to convert original problem into a multistage optimization problem, in which a new normalized time variable is adopted on the combination of the subinterval length. Then the rationalized Haar function approximation method, in which an auxiliary function is introduced to dispose path constraints, is used to transform the multistage problem into a nonlinear programming. Furthermore, an adaptive strategy proposed on the basis of errors is adopted to regulate the order of Haar function vectors. Finally, the nonlinear programming for ASP flooding is solved by sequential quadratic programming. To illustrate the performance of proposed method,the experimental comparison method and control vector parameterization(CVP) method are introduced to optimize the original problem directly. By contrastive analysis of results, the accuracy and efficiency of proposed method are confirmed.
文摘Recently we have reported a new method of rational approximation of the sinc function obtained by sampling and the Fourier transforms. However, this method requires a trigonometric multiplier that originates from the shifting property of the Fourier transform. In this work, we show how to represent the Fourier transform of a function <em>f</em>(<em>t</em>) in form of a ratio of two polynomials without any trigonometric multiplier. A MATLAB code showing algorithmic implementation of the proposed method for rational approximation of the Fourier transform is presented.
基金supported by the National Nature Science Foundation of China(No.11571362)Fundamental Research Funds for the Central Universities(No.2652018054).
文摘In the present note,we consider the problem:how many interpolation nodes can be deleted from the Newman-type rational function such that the convergence rate still achieve.
基金supported by the Department of Energy (No.DE-FG02-03ER25587)the Office of Naval Research(No.N00014-01-1-0674)an Alfred P.Sloan Research Fellowship and a startup grant from University of Texas at Austin
文摘Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed： one uses the contour integral representation and conformal real〉 ping, and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic structure calculations.
