DEGREE OF APPROXIMATION ASSOCIATED WITH SOME ELLIPTIC OPERATORS AND ITS APPLICATIONS

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.

DEGREE OF APPROXIMATION BY SUPERPOSITIONS OF A SIGMOIDAL FUNCTION

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.

Degree of Approximation of Conjugate of Signals (Functions) by Lower Triangular Matrix Operator

In the present paper, an attempt is made to obtain the degree of approximation of conjugate of functions (signals) belonging to the generalized weighted W(LP, ξ(t)), (p ≥ 1)-class, by using lower triangular matrix operator of conjugate series of its Fourier series.

A SHARP ESTIMATE ON THE DEGREE OF APPROXIMATION TO FUNCTIONS OF BOUNDED VARIATION BY CERTAIN OPERATORS

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.

ON THE EXACT DEGREE OF APPROXIMATION BY HERMITE-FEJER INTERPOLATION BASED ON THE LAGUERRE ABSCISSAS

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.

ON THE DEGREE OF APPROXIMATION BY WAVELET EXPANSIONS

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.

Theory of Approximate Reasoning in Two-Valued Predicate Logic Based on the Quasi-truth Degrees

Based on the theory of the quasi-truth degrees in two-valued predicate logic, some researches on approximate reasoning are studied in this paper. The relation of the pseudo-metric between first-order formulae and the quasi-truth degrees of first-order formulae is discussed, and it is proved that there is no isolated point in the logic metric space (F, ρ ). Thus the pseudo-metric between first-order formulae is well defined to develop the study about approximate reasoning in the logic metric space (F, ρ ). Then, three different types of approximate reasoning patterns are proposed, and their equivalence under some condition is proved. This work aims at filling in the blanks of approximate reasoning in quantitative predicate logic.

APPROXIMATE COMMON DIVISORS OF POLYNOMIALS AND DEGREE REDUCTION FOR RATIONAL CURVES

Abstract This paper deals with how to perturb a given set of polynomials so as to include a common linear factor. An algorithm is derived for determining such a set of perturbation polynomials which are subject to certain constrains at the endpoints of a prescribed parametric interval and minimized in a certain sense. This result can be combined with subdivision technique to obtain a continuous piecewise approximation to a rational curve.

The Degree of Approximation by(E,q)(C,α,β)Means in Orlicz Spaces

In this paper,we study the trigonometric approximation problems of functions which belong to the Lipαclass,the Lip(ξ(t))class,and the W(L_(M)^(*);ξ(t))class in Orlicz spaces by using the tools Hölder inequality in Orlicz spaces,the second mean value theorem for integrals,and(E,q)(C,α,β)means etc.At the same time,we give the corresponding degree of approximation.

ASYMPTOTIC APPROXIMATION OF FUNCTIONS AND THEIR DERIVATIVES BY GENERALIZED BASKAKOV-SZAZS-DURRMEYER OPERATORS

We present the complete asymptotic expansion for a generalization of the Baskakov-Szasz-Durrmeyer operators and their derivatives.

ON STRONG APPROXIMATION APPLIED TO POST-WIDDER OPERATORS

We introduce modified Post-Widder operators in polynomial weighted spaces of differentiable functions and we study strong approximation for them.

ON THE SATURATION OF L_w^p-APPROXIMATION BY (O-q'-q) TYPE HERMITE-FEJER INTERPOLATING POLYNOMIALS

The 'o' saturation theorem and the degree of Lwp, approximation by (0 - q' - q) type Hermite-Fejer interpolating polynomials for mean convergence are obtained.

A quadratic programming method for optimal degree reduction of Bézier curves with G^1-continuity

This paper presents a quadratic programming method for optimal multi-degree reduction of B6zier curves with G^1-continuity. The L2 and I2 measures of distances between the two curves are used as the objective functions. The two additional parameters, available from the coincidence of the oriented tangents, are constrained to be positive so as to satisfy the solvability condition. Finally, degree reduction is changed to solve a quadratic problem of two parameters with linear constraints. Applications of degree reduction of Bezier curves with their parameterizations close to arc-length parameterizations are also discussed.

Approximation of Generalized Szász-Mirakjan Operator

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].

Generalized Szász-Mirakjan Operator Approximation

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.

Approximation Properties of a Special Class of Mathematical Expectation Operators

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.

A New Class of Generalized Landau Linear Positive Operator Sequence and Its Properties of Approximation

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).

On the Degree of Approximation by Spherical Translations

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.

On the Degree of Approximation of Continuous Functions by Means of Fourier Series in the Holder Metric

In this paper we prove two theorems on the degree of approximation of continuous functions by matrix means related to partial sums of a Fourier series in the Holder metric.These theorems can be taken as counterparts of those previously obtained by T.Singh[3].

半无限介质多自由度频响函数离散时间有理近似的稳定参数识别

离散时间有理近似函数是将半无限土频响函数转化为时域模型的重要工具,离散时间有理近似函数和时域模型具有相同的稳定性和精度。目前关于离散时间有理近似函数的研究只针对于单自由度系统。该文基于线性控制理论,给出了多自由度有理近似系统的稳定条件。将稳定性条件与遗传-序列二次算法相结合,开发了多自由度频响函数参数辨识方法,保证了多自由度系统的稳定性和精度。不同维度的多自由度有理近似系统的数值仿真验证了该文方法可以保证多自由度有理近似系统的稳定性和精度。