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EXISTENCE AND LOCAL BEHAVIOR OF NONDIAGONAL BIVARIATE QUADRATIC FUNCTION APPROXIMATION 认领 引用
1
作者 ZhengChengde WangRenhong 《Applied Mathematics(A Journal of Chinese Universities)》 2003年第4期442-452,共11页
This paper analyses the local behavior of the simple off-diagonal bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin.It is shown that the simpl... This paper analyses the local behavior of the simple off-diagonal bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin.It is shown that the simple off-diagonal bivariate quadratic Hermite-Padé form always defines a bivariate quadratic function and that this function is analytic in a neighbourhood of the origin.Numerical examples compare the obtained results with the approximation power of diagonal Chisholm approximant and Taylor polynomial approximant. 展开更多
关键词 Hermite-Padé approximation bivariate function approximation bivariate analytic function
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Optimization for ASP flooding based on adaptive rationalized Haar function approximation 认领 引用
2
作者 Yulei Ge Shurong Li Xiaodong Zhang 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2018年第8期1758-1765,共8页
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
关键词 Alkali-surfactant-polymer flooding Optimization Enhanced oil recovery Mathematical modeling Rationalized Haar function approximation Adaptive strategy
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The Existence and Local Behavior of the Bivariate Quadratic Function Approximation 认领 引用
3
作者 ZHENG Cheng-de 《Chinese Quarterly Journal of Mathematics》 北大核心 2006年第1期110-114,共5页
This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It is shown that the bivariate quadratic Herm... This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It is shown that the bivariate quadratic Hermite-Padé form always defines a bivariate quadratic function and that this function is analytic in a neighborhood of the origin. 展开更多
关键词 Hermite-Padé approximation bivariate function approximation bivariate analytic function
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ON VECTOR VALUED FUNCTION APPROXIMATION USING A PEAK NORM 认领 引用
4
作者 G.A.Watson 《Analysis in Theory and Applications》 1996年第2期1-12,共12页
A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some f... A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some families of simultaneous best approximation problems. 展开更多
关键词 ON VECTOR VALUED FUNCTION APPROXIMATION USING A PEAK NORM 任气
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Complex Function Approximation Based on Multi-ANN Approach 认领 引用
5
作者 Li Renhou & Gao Feng 《Journal of Systems Engineering and Electronics》 EI 1995年第2期22-31,共10页
This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ab... This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems. 展开更多
关键词 Backpropagation algorithm Multilayer perception Complex function approximation Input space partitioning.
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Approximation Properties of Newman Type Interpolation Rational Functions with Fewer Nodes 认领 引用
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作者 Laiyi Zhu Xingjun Zhao 《Analysis in Theory and Applications》 CSCD 2023年第4期378-384,共7页
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.
关键词 Rational function approximation Newman-type rational approximation interpolation nodes convergence rate
Greedy feature replacement for online value function approximation 认领 引用
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作者 Feng-fei ZHAO Zheng QIN +2 位作者 Zhuo SHAO Jun FANG Bo-yan REN 《Journal of Zhejiang University-Science C(Computers and Electronics)》 2014年第3期223-231,共9页
Reinforcement learning(RL) in real-world problems requires function approximations that depend on selecting the appropriate feature representations. Representational expansion techniques can make linear approximators ... Reinforcement learning(RL) in real-world problems requires function approximations that depend on selecting the appropriate feature representations. Representational expansion techniques can make linear approximators represent value functions more effectively; however, most of these techniques function well only for low dimensional problems. In this paper, we present the greedy feature replacement(GFR), a novel online expansion technique, for value-based RL algorithms that use binary features. Given a simple initial representation, the feature representation is expanded incrementally. New feature dependencies are added automatically to the current representation and conjunctive features are used to replace current features greedily. The virtual temporal difference(TD) error is recorded for each conjunctive feature to judge whether the replacement can improve the approximation. Correctness guarantees and computational complexity analysis are provided for GFR. Experimental results in two domains show that GFR achieves much faster learning and has the capability to handle large-scale problems. 展开更多
关键词 Reinforcement learning Function approximation Feature dependency Online expansion Feature replacement
RBF neural network based on q-Gaussian function in function approximation 认领 引用 被引量：2
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作者 Wei ZHAO Ye SAN 《Frontiers of Computer Science》 CSCD 2011年第4期381-386,共6页
To enhance the generalization performance of radial basis function （RBF） neural networks, an RBF neural network based on a q-Gaussian function is proposed. A q-Gaussian function is chosen as the radial basis functio... To enhance the generalization performance of radial basis function （RBF） neural networks, an RBF neural network based on a q-Gaussian function is proposed. A q-Gaussian function is chosen as the radial basis function of the RBF neural network, and a particle swarm optimization algorithm is employed to select the parameters of the network. The non-extensive entropic index q is encoded in the particle and adjusted adaptively in the evolutionary process of population. Simulation results of the function approximation indicate that an RBF neural network based on q-Gaussian function achieves the best generalization performance. 展开更多
关键词 radial basis function （RBF） neural network,q-Gaussian function particle swarm optimization algo-rithm function approximation
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Control of air pollution sources based on method of consecutive functional approximation 认领 引用
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作者 Filonchyk Mikalai YAN Hao-wen +1 位作者 Hurynovich Volha Stroi Anton 《Journal of Measurement Science and Instrumentation》 CAS CSCD 2016年第4期375-378,共4页
In this article the approach was used to coherent assessment based on the intensity of air pollution sources impact on the impurity concentration at a few fixed points to monitor air quality. The numerical analogue of... In this article the approach was used to coherent assessment based on the intensity of air pollution sources impact on the impurity concentration at a few fixed points to monitor air quality. The numerical analogue of Duhamers theorem was used to describe processes of propagation of impurity in the atmosphere. Such approach allows you to count on essential increase of calculation accuracy based on mathematical models of reasonable complexity. The inverse problem of pollutants propagation in the atmosphere based on the measurements of the impurity concentration in stationary or mobile control points was solved by the sequential function approximation The solution was presented in the form of a digital filter. 展开更多
关键词 air pollution inverse problem sequential function approximation the equation of turbulent diffusion
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ON THE POINTWISE ESTIMATIONS OF APPROXIMATION OF FUNCTIONS AND THEIR DERIVATIVES BY HERMITE INTERPOLATION 认领 引用 被引量：1
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作者 Tingfan Xie Ziyu Wang China Institute of Metrology, China Henan University, China 《Analysis in Theory and Applications》 1994年第3期45-55,共11页
The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen-... The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen- eral. 展开更多
关键词 Math ON THE POINTWISE ESTIMATIONS OF APPROXIMATION OF FUNCTIONS AND THEIR DERIVATIVES BY HERMITE INTERPOLATION 石瓦
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How to Extend the Bridge Density Functional Approximation to the Confined Non-hard Sphere Fluid 认领 引用
11
作者 Shi-qi Zhou 《Chinese Journal of Chemical Physics》 SCIE EI CAS 北大核心 2006年第4期319-324,共6页
A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simp... A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simple, quantitatively accurate in a wide range of coexistence phase and external field parameters. Especially, the DFT approach only needs a second order direct correlation function （DCF） of the coexistence bulk fluid as input, and is therefore applicable to the subcritical temperature region. The present theoretical method can be regarded as a non-uniform counterpart of the thermodynamic perturbation theory, in which it is not at the level of the free energy but at the level of the second order DCF.the National Natural Science Foundation of China （No. 20546004） and the Natural Science Foundation of Education Department of Hunan Province （No.04C711）. 展开更多
关键词 Density functional theory Bridge density functional approximation Hard sphere fluid Correlation function
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Bridge density functional approximation for non-uniform hard core repulsive Yukawa fluid 认领 引用
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作者 周世琦 《Chinese Physics B》 SCIE EI CAS 2008年第10期3812-3821,共10页
In this work, a bridge density functional approximation （BDFA） （J. Chem. Phys. 112, 8079 （2000）） for a nonuniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa （HCRY） fluid. It is f... In this work, a bridge density functional approximation （BDFA） （J. Chem. Phys. 112, 8079 （2000）） for a nonuniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa （HCRY） fluid. It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid. A new bridge functional approximation is proposed, which can accurately predict the radial distribution function of the bulk HCRY fluid. With the new bridge functional approximation and its associated bulk second order direct correlation function as input, the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields, and the theoretical predictions are in good agreement with the corresponding simulation data. The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase, and the adsorption properties of the HCRY fluid, which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail. 展开更多
关键词 bridge density functional approximation radial distribution function colloid density distribution
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A SHARP ESTIMATE ON THE DEGREE OF APPROXIMATION TO FUNCTIONS OF BOUNDED VARIATION BY CERTAIN OPERATORS 认领 引用 被引量：1
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作者 Vijay Gupta 《Analysis in Theory and Applications》 1995年第3期106-107,共2页
Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
关键词 A SHARP ESTIMATE ON THE DEGREE OF APPROXIMATION TO FUNCTIONS OF BOUNDED VARIATION BY CERTAIN OPERATORS
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ON SHAPE PRESERVING EXTENSION AND APPROXIMATION OF FUNCTIONS 认领 引用
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作者 卢旭光 《Analysis in Theory and Applications》 1992年第2期67-88,共22页
We establish the concept of shapes of functions by using partial differential inequalites. Our definition about shapes includes some usual shapes such as convex,subharmonic,etc.,and gives many new shapes of functions.... We establish the concept of shapes of functions by using partial differential inequalites. Our definition about shapes includes some usual shapes such as convex,subharmonic,etc.,and gives many new shapes of functions.The main results show that the shape preserving approxi- mation has close relation to the shape preserving extension.One of our main results shows that if f∈C(Ω)has some shape defined by our definition,then f can be uniformly approximated by polynomials P_n ∈p_n(n∈N)which have the same shape in Ω,and the degree of the ap- proximation is Cω(f,n-β)with constants C,β>0. 展开更多
关键词 ON SHAPE PRESERVING EXTENSION AND APPROXIMATION OF FUNCTIONS
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An Approximation Method for Singular Trudinger-Moser Inequality 认领 引用
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作者 ZHU Maochun XU Wenyan JIANG Rou 《应用数学》 北大核心 2025年第1期64-70,共7页
In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to... In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball. 展开更多
关键词 Singular Trudinger-Moser inequality Approximation functional Concentration level
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Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach 认领 引用
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作者 Shenquan Wang Wenchengyu Ji +2 位作者 Yulian Jiang Yanzheng Zhu Jian Sun 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第4期996-1006,共11页
This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By i... This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples. 展开更多
关键词 Equivalent reciprocal combination technique quadratic function convex approximation approach stability timevarying delay
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DEGREE OF APPROXIMATION BY SUPERPOSITIONS OF A SIGMOIDAL FUNCTION 认领 引用 被引量：18
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作者 Chen Debao 《Analysis in Theory and Applications》 1993年第3期17-28,共12页
In this paper we study the degree of approximation by superpositions of a sigmoidal function.We mainly consider the univariate case.If f is a continuous function,we prove that for any bounded sigmoidal function σ,d_... In this paper we study the degree of approximation by superpositions of a sigmoidal function.We mainly consider the univariate case.If f is a continuous function,we prove that for any bounded sigmoidal function σ,dn,σ(f)≤‖σ‖ω(f,1/(n+1)).For the Heaviside function H(x),we prove that dn,H(f)≤ω(f,1/(2(n+1))). If f is a continuous funnction of bounded variation,we prove that dn,σ(f)≤‖σ‖/(n+1)V(f)and dn,H(f)≤ 1/(2(n+1))V(f).For he Heaviside function,the coefficient 1 and the approximation orders are the best possible.We compare these results with the classical Jackson and Bernstein theorems,and make some conjec- tures for further study. 展开更多
关键词 DEGREE OF APPROXIMATION BY SUPERPOSITIONS OF A SIGMOIDAL FUNCTION
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SIMULTANEOUSE APPROXIMATION TO A DIFFERENTIABLE FUNCTION AND ITS DERIVATIVES BY LAGRANGE INTERPOLATING POLYNOMIALS 认领 引用 被引量：1
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作者 T.F.Xie S.P.Zhou 《Analysis in Theory and Applications》 1994年第4期100-109,共10页
This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |fk(x)-P_nk(f,x)|=O(1)△_nq-k(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of... This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |fk(x)-P_nk(f,x)|=O(1)△_nq-k(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next). 展开更多
关键词 SIMULTANEOUSE APPROXIMATION TO A DIFFERENTIABLE FUNCTION AND ITS DERIVATIVES BY LAGRANGE INTERPOLATING POLYNOMIALS APPI Zr
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PADE APPROXIMANTS AS LIMITS OF RATIONAL FUNCTIONS OF BEST APPROXIMATION IN ORLICZ SPACE 认领 引用
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作者 Li Jialiang Central China Normal University, China Department of Mathematics Central Normal University 《Analysis in Theory and Applications》 1994年第2期74-82,共9页
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
关键词 Rational Math PADE APPROXIMANTS AS LIMITS OF RATIONAL FUNCTIONS OF BEST APPROXIMATION IN ORLICZ SPACE AS
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ON APPROXIMATION OF A FUNCTION AND ITS DERIVATIVES BY A POLYNOMIAL AND ITS DERIVATIVES 认领 引用
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作者 T.Kilgore J.Szabados 《Analysis in Theory and Applications》 1994年第3期93-103,共11页
Let g∈C^q[-1, 1] be such that g(k)(±1)=0 for k=0,…,q. Let P_n be an algebraic polynomial of degree at most n, such that P_n(k)(±1)=0 for k=0,…,[_2~ (q+1)]. Then P_n and its derivatives P_n(k) fo... Let g∈C^q[-1, 1] be such that g(k)(±1)=0 for k=0,…,q. Let P_n be an algebraic polynomial of degree at most n, such that P_n(k)(±1)=0 for k=0,…,[_2~ (q+1)]. Then P_n and its derivatives P_n(k) for k≤q well approximate g and its respective derivatives, provided only that P_n well approxi- mates g itself in the weighted norm ‖g(x)-P_n(x) (1-x^2)1/2~q‖ This result is easily extended to an arbitrary f∈C^q[-1, 1], by subtracting from f the polynomial of minnimal degree which interpolates f(0)…,f(q) at±1. As well as providing easy criteria for judging the simultaneous approximation properties of a given Polynomial to a given function, our results further explain the similarities and differences between algebraic polynomial approximation in C^q[-1, 1] and trigonometric polynomial approximation in the space of q times differentiable 2π-periodic functions. Our proofs are elementary and basic in character, permitting the construction of actual error estimates for simultaneous approximation proedures for small values of q. 展开更多
关键词 ON APPROXIMATION OF A FUNCTION AND ITS DERIVATIVES BY A POLYNOMIAL AND ITS DERIVATIVES ITS
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