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DEGREE OF APPROXIMATION ASSOCIATED WITH SOME ELLIPTIC OPERATORS AND ITS APPLICATIONS 被引量:8
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作者 Xinlong Zhou(University of Duisburg, Germany) 《Analysis in Theory and Applications》 1995年第2期9-29,共21页
The Jackson-type estimates by using some elliptic operators will be achieved. These results will be used to characterize the regularity of some elliptic operators by means of the approximation degree and the saturatio... The Jackson-type estimates by using some elliptic operators will be achieved. These results will be used to characterize the regularity of some elliptic operators by means of the approximation degree and the saturation class of the multivariate Bernstein operators as well. 展开更多
关键词 degree OF APPROXIMATION ASSOCIATED WITH SOME ELLIPTIC OPERATORS AND ITS APPLICATIONS II ITS
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DEGREE OF APPROXIMATION BY SUPERPOSITIONS OF A SIGMOIDAL FUNCTION 被引量:14
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作者 Chen Debao (University of Texas at Austin,USA) 《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,d_(n,σ)(f)≤‖σ‖ω(f,1/(n+1)).For the Heaviside function H(x),we prove that d_(n,H)(f)≤ω(f,1/(2(n+1))). If f is a continuous funnction of bounded variation,we prove that d_(n,σ)(f)≤‖σ‖/(n+1)V(f)and d_(n,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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A SHARP ESTIMATE ON THE DEGREE OF APPROXIMATION TO FUNCTIONS OF BOUNDED VARIATION BY CERTAIN OPERATORS 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 THE EXACT DEGREE OF APPROXIMATION BY HERMITE-FEJER INTERPOLATION BASED ON THE LAGUERRE ABSCISSAS
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作者 Shen Yunhai Sun Xiehua 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第4期405-410,共6页
For the nonpositive Hermite-Fejér interpolation based on the Laguerre abscissas, a pointwise two-sided estimate of the degree of approximation in the aleatoric interval [0, A] is first established.
关键词 Hermite-Fejér interpolation Laguerre abscissas two-sided estimate degree of approximation.
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ON THE DEGREE OF APPROXIMATION BY WAVELET EXPANSIONS 被引量:15
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作者 Sun Xiehua (China Institute of Metrology, China) 《Analysis in Theory and Applications》 1998年第1期81-90,共0页
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
关键词 ON THE degree OF APPROXIMATION BY WAVELET EXPANSIONS
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Improved Approximate Minimum Degree Ordering Method and Its Application for Electrical Power Network Analysis and Computation 被引量:1
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作者 Jian Guo Hong Liang +3 位作者 Songpu Ai Chao Lu Haochen Hua Junwei Cao 《Tsinghua Science and Technology》 SCIE EI CAS CSCD 2021年第4期464-474,共11页
Electrical power network analysis and computation play an important role in the planning and operation of the power grid,and they are modeled mathematically as differential equations and network algebraic equations.Th... Electrical power network analysis and computation play an important role in the planning and operation of the power grid,and they are modeled mathematically as differential equations and network algebraic equations.The direct method based on Gaussian elimination theory can obtain analytical results.Two factors affect computing efficiency:the number of nonzero element fillings and the length of elimination tree.This article constructs mapping correspondence between eliminated tree nodes and quotient graph nodes through graph and quotient graph theories.The Approximate Minimum Degree(AMD)of quotient graph nodes and the length of the elimination tree nodes are composed to build an Approximate Minimum Degree and Minimum Length(AMDML)model.The quotient graph node with the minimum degree,which is also the minimum length of elimination tree node,is selected as the next ordering vector.Compared with AMD ordering method and other common methods,the proposed method further reduces the length of elimination tree without increasing the number of nonzero fillings;the length was decreased by about 10%compared with the AMD method.A testbed for experiment was built.The efficiency of the proposed method was evaluated based on different sizes of coefficient matrices of power flow cases. 展开更多
关键词 approximate Minimum degree and Minimum Length(AMDML) electrical power network analysis elimination tree numerical solution ordering method
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Application of Short-wave Near-infrared Reflectance Spectroscopy in Controlling Extract of Fructus Cnidii Using Supercritical Carbon Dioxide 被引量:1
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作者 MI Hong GUO Ye +4 位作者 LI Wen-liang Qu Nan DOU Ying REN Yu-qiu REN Yu-lin 《Chemical Research in Chinese Universities》 SCIE CAS CSCD 2007年第1期116-119,共4页
Fructus cnidii (Chinese name shechuangzi) is the fruit produced by Cnidium monnieri (L.) Cusson (Umbelliferae). It is a perennial herb that is used to treat skin-related diseases and gynecopathyell. Recent pharm... Fructus cnidii (Chinese name shechuangzi) is the fruit produced by Cnidium monnieri (L.) Cusson (Umbelliferae). It is a perennial herb that is used to treat skin-related diseases and gynecopathyell. Recent pharmacological studies have revealed crude extracts or components isolated from fructus cnidii possess antiallergic, antipruritic, antidermatophytic, antibacterial, antifungal, and antiosteoporotic activities. Osthole and imperatorin are the major compounds present in shechuangzi. They are often used as standards for the evaluation of the quality of shechuangzi products. 展开更多
关键词 Fructus cnidii Supercfitical carbon dioxide Short-wave near-infrared diffuse reflectance spectrum Artificial neural network degree of approximation
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ASYMPTOTIC APPROXIMATION OF FUNCTIONS AND THEIR DERIVATIVES BY GENERALIZED BASKAKOV-SZAZS-DURRMEYER OPERATORS 被引量:1
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作者 Ulrich Abel Vijay Gupta Mircea Ivan 《Analysis in Theory and Applications》 2005年第1期15-26,共12页
We present the complete asymptotic expansion for a generalization of the Baskakov-Szasz-Durrmeyer operators and their derivatives.
关键词 approximation by positive operators rate of convergence degree of approximation asymptotic expansion Stirling numbers
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Approximation of Generalized Szász-Mirakjan Operator
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作者 程海来 《Chinese Quarterly Journal of Mathematics》 CSCD 1995年第3期23-28,共6页
In this paper, the author define a kind of generalized Szasz-Mirakjan operator and discuss its convergence and degree of the approximation,extend some results got by J. Grof[1] and Z. Ditzian[2].
关键词 approximation degree positive operator uniform convergence pointwise convergence
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Generalized Szász-Mirakjan Operator Approximation
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作者 程海来 《Chinese Quarterly Journal of Mathematics》 CSCD 1993年第3期24-29,共6页
In this paper we shall defin a kind of generahzed Szász-Mirakjan operator and discuss its convergence and degree of approximation,extend some results got by J.Grof and Z.Ditzian.
关键词 degree of approximation positive operator uniform convergence pointwise convergence
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ON STRONG APPROXIMATION APPLIED TO POST-WIDDER OPERATORS
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作者 Lucyna Rempulska Mariola Skorupka 《Analysis in Theory and Applications》 2006年第2期172-182,共11页
We introduce modified Post-Widder operators in polynomial weighted spaces of differentiable functions and we study strong approximation for them.
关键词 Post-Widder operator strong approximation degree of approximation
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ON THE SATURATION OF L_w^p-APPROXIMATION BY (O-q'-q) TYPE HERMITE-FEJER INTERPOLATING POLYNOMIALS
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作者 LiJiangbo ShengBaohuai 《Analysis in Theory and Applications》 2004年第3期252-264,共13页
The 'o' saturation theorem and the degree of Lwp, approximation by (0 - q' - q) type Hermite-Fejer interpolating polynomials for mean convergence are obtained.
关键词 Hermite-Fejer interpolation degree of approximation saturation order
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Approximation Properties of a Special Class of Mathematical Expectation Operators
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作者 陈历敏 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第2期62-69, ,共8页
In this paper we study the local measure of approximation of a class of special mathematical expectation operators to Lipschitz class of functions by probabilistic method. The some well known operators (e. g., the Ber... In this paper we study the local measure of approximation of a class of special mathematical expectation operators to Lipschitz class of functions by probabilistic method. The some well known operators (e. g., the Bernstein, Bascakov and Szasz-Mirakjan operators etc) are special cases of a class of the mathematical expetation operators. 展开更多
关键词 OPERATOR degree of approximation Lipschitz class of functions
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A New Class of Generalized Landau Linear Positive Operator Sequence and Its Properties of Approximation
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作者 陈湛本 石济民 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第1期29-43, ,共15页
In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the wh... In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the whole real axis. The properties of approximation are studied and their asymptotic formulae are presented. These results show that their degrees of approximation are the best among existing operator sequences of Landau type, for example, their degrees of approximation for C 2[0, 1] are O(1/n 2) but corresponding degree of ordinary Landau operators are only O(1/n). 展开更多
关键词 generalized Landau linear positive operators degree of approximation asymptotic formula
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On the Degree of Approximation by Spherical Translations
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作者 Bao-huai Sheng 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2006年第4期671-680,共10页
The degree of approximation of spherical functions by the translations formed by a function defined on the unit sphere is dealt with. A kind of Jackson inequality is established under the condition that none of the L^... The degree of approximation of spherical functions by the translations formed by a function defined on the unit sphere is dealt with. A kind of Jackson inequality is established under the condition that none of the L^2(S^q) norms of the orthogonal projection operators of the translated function are zeros. In the present paper we show that the spherical translations share the same degree of approximation as that of spherical harmonics. 展开更多
关键词 Spherical harmonics translation class degree of approximation
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Degrees of freedom in low rank matrix estimation
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作者 YUAN Ming 《Science China Mathematics》 SCIE CSCD 2016年第12期2485-2502,共18页
The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for thes... The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results. 展开更多
关键词 degrees of freedom low rank matrix approximation model selection nuclear norm penalization reduced rank regression Stein's unbiased risk estimator
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On Bounded Variation Functions by General MKZD Operators
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作者 Vijay GUPTA 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第8期1457-1462,共6页
In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer-Knig-Zeller-Durrmeyer operators.
关键词 approximation by positive operators rate of convergence degree of approximation functions of bounded variation total variation
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