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1.
In this paper the least-squares mixed finite element is considered for solving secondorder elliptic problems in two dimensional domains. The primary solution u and the flux er are approximated using finite element spaces consisting of piecewise polynomials of degree k and r respectively. Based on interpolation operators and an auxiliary projection,superconvergent H^1-error estimates of both the primary solution approximation uh and the flux approximation σh are obtained under the standard quasi-uniform assumption on finite element partition. The superconvergence indicates an accuracy of O(h^r 2) for the least-squares mixed finite element approximation if Raviart-Thomas or Brezzi-DouglasFortin-Marini elements of order r are employed with optimal error estimate of O(h^r l).  相似文献   

2.
We establish the pointwise approximation theorems for the combinations of Bernstein polynomials by the rth Ditzian-Totik modulus of smoothness wФ^r(f, t) where Ф is an admissible step-weight function. An equivalence relation between the derivatives of these polynomials and the smoothness of functions is also obtained.  相似文献   

3.
Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.  相似文献   

4.
Suppose that either the outer mapping function of a domain D has continuous second derivatives or D is a strictly star domain. In this paper we first establish two inequalities concerning polynomials at Fejer's points with multiplicity (3 + 1). Using these two inequalities, we obtain the order of approximation in Lp(dD), 0相似文献   

5.
In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.  相似文献   

6.
The polynomials related with cubic Hermite-Padéapproximation to the exponentialfunction are investigated which have degrees at most n,m,s respectively.A connectionis given between the coefficients of each of the polynomials and certain hypergeometricfunctions,which leads to a simple expression for a polynomial in a special case.Contourintegral representations of the polynomials are given.By using of the saddle point methodthe exact asymptotics of the polynomials are derived as n,m,s tend to infinity throughcertain ray sequence.Some further uniform asymptotic aspects of the polynomials are alsodiscussed.  相似文献   

7.
We study the optimal order of approximation for |x|α (0 < α < 1) by Lagrange interpolation polynomials based on Chebyshev nodes of the first kind. It is proved that the Jackson order of approximation is attained.  相似文献   

8.
Lagrange插值逼近导数的平均收敛   总被引:1,自引:0,他引:1  
<正>We consider the rate of mean convergence of derivatives by Lagrange interpolation operators L_n(f,x) based on the zeros of Chebyshev polynomials of the first kind.A sharp estimate of the derivative of L_n(f,x)—f(x) in terms of the error of best approximation by polynomials of degree n is derived.  相似文献   

9.
Γ.Ц.Тумаркин established the weighted mean approximation by polynomials to functions of class D on a circle |z| =1. Here we have estimated the degree of weighted mean approximation.C. Я.Алълерestablished the estimation of the degree of mean approximation to functions of class Ep(1p(1≤p<∞) on a rectifiable curve.  相似文献   

10.
Non-uniform algebraic-trigonometric B-splines shares most of the properties as those of the usual polynomial B-splines. But they are not orthogonal. We construct an orthogonal basis for the n-order(n ≥ 3) algebraic-trigonometric spline space in order to resolve the theoretical problem that there is not an explicit orthogonal basis in the space by now. Motivated by the Legendre polynomials, we present a novel approach to define a set of auxiliary functions,which have simple and explicit expressions. Then the proposed orthogonal splines are given as the derivatives of these auxiliary functions.  相似文献   

11.
作为Bernstein-Durrmeyer多项式的推广,定义单纯形上的Bernstein-Durrmeyer型多项式.以最佳多项式逼近为度量,给出Bernstein-Durrmeyer型多项式Lp逼近阶的估计,并且以一个逆向不等式的形式建立其Lp逼近的逆定理,从而用最佳多项式逼近刻画该多项式Lp逼近的特征.所获结果包含了多元Bernstein-Durrmeyer多项式的相应结果.  相似文献   

12.
Summary. The paper presents results on the approximation of functions which solve an elliptic differential equation by operator adapted systems of functions. Compared with standard polynomials, these operator adapted systems have superior local approximation properties. First, the case of Laplace's equation and harmonic polynomials as operator adapted functions is analyzed and rates of convergence in a Sobolev space setting are given for the approximation with harmonic polynomials. Special attention is paid to the approximation of singular functions that arise typically in corners. These results for harmonic polynomials are extended to general elliptic equations with analytic coefficients by means of the theory of Bergman and Vekua; the approximation results for Laplace's equation hold true verbatim, if harmonic polynomials are replaced with generalized harmonic polynomials. The Partition of Unity Method is used in a numerical example to construct an operator adapted spectral method for Laplace's equation that is based on approximating with harmonic polynomials locally. Received May 26, 1997 / Revised version received September 21, 1998 / Published online September 7, 1999  相似文献   

13.
单纯形上的Stancu多项式与最佳多项式逼近   总被引:8,自引:2,他引:6  
曹飞龙  徐宗本 《数学学报》2003,46(1):189-196
作为Bernstein多项式的推广,本文定义单纯形上的多元Stancu多项式.以最佳多项式逼近为度量,建立Stancu多项式对连续函数的逼近定理与逼近阶估计,给出Stancu多项式的一个逼近逆定理,从而用最佳多项式逼近刻划Stancu多项式的逼近特征.  相似文献   

14.
We find the polynomials of the best one-sided approximation to the Heaviside and sign functions. The polynomials are obtained by Hermite interpolation at the zeros of some Jacobi polynomials. Also we give an estimate of the error of approximation and characterize the extremal points of the convex set of the best approximants.  相似文献   

15.
Szegő polynomials are orthogonal with respect to an inner product on the unit circle. Numerical methods for weighted least-squares approximation by trigonometric polynomials conveniently can be derived and expressed with the aid of Szegő polynomials. This paper discusses the conditioning of several mappings involving Szegő polynomials and, thereby, sheds light on the sensitivity of some approximation problems involving trigonometric polynomials. This Research supported in part by NSF grant DMS-0107858.  相似文献   

16.
研究了复赋范空间中具限制系数的广义多项式集G对无穷序列的最佳同时逼近问题,得到了特征定理;当G是复RS集时还得到了惟一性定理.  相似文献   

17.
Dual Bernstein polynomials of one or two variables have proved to be very useful in obtaining Bézier form of the L 2-solution of the problem of best polynomial approximation of Bézier curve or surface. In this connection, the Bézier coefficients of dual Bernstein polynomials are to be evaluated at a reasonable cost. In this paper, a set of recurrence relations satisfied by the Bézier coefficients of dual bivariate Bernstein polynomials is derived and an efficient algorithm for evaluation of these coefficients is proposed. Applications of this result to some approximation problems of Computer Aided Geometric Design (CAGD) are discussed.  相似文献   

18.
In this paper, an approximation of functions of extensive classes set on a countable unit of segments of a real axis using the entire functions of exponential type is considered. The higher the type of the approximating function is, the higher the rate of approximation near segment ends can be made, compared with their inner points. The general approximation scale, which is nonuniform over its segments, depending on the type of the entire function, is similar to the scale set out for the first time in the study of the approximation of the function by polynomials. For cases with one segment and its approximation by polynomials, this scale has allowed us to connect the so-called direct theorems, which state a possible rate of smooth function approximation by polynomials, and the inverse theorems, which give the smoothness of a function approximated by polynomials at a given rate. The approximations by entire functions on a countable unit of segments for the case of Hölder spaces have been studied by the authors in two preceding papers. This paper significantly expands the class of spaces for the functions, which are used to plot an approximation that engages the entire functions with the required properties.  相似文献   

19.
球面带形平移网络逼近的Jackson定理   总被引:2,自引:0,他引:2  
盛宝怀 《数学进展》2006,35(3):325-335
研究了球面带型平移网络逼近阶用球面调和多项式的最佳逼近及光滑模的刻画问题.借助于球调和多项式的最佳逼近多项式和Riesz平均构造出了单位球面Sq上的带形平移网络,并建立了球面带形平移网络对Lp(Sq)中函数一致逼近的Jackson型定理.所得结果表明球面带形平移网络可以达到球调和多项式的逼近阶.  相似文献   

20.
Summary. This paper studies polynomials used in polynomial preconditioning for solving linear systems of equations. Optimum preconditioning polynomials are obtained by solving some constrained minimax approximation problems. The resulting residual polynomials are referred to as the de Boor-Rice and Grcar polynomials. It will be shown in this paper that the de Boor-Rice and Grcar polynomials are orthogonal polynomials over several intervals. More specifically, each de Boor-Rice or Grcar polynomial belongs to an orthogonal family, but the orthogonal family varies with the polynomial. This orthogonality property is important, because it enables one to generate the minimax preconditioning polynomials by three-term recursive relations. Some results on the convergence properties of certain preconditioning polynomials are also presented. Received February 1, 1992/Revised version received July 7, 1993  相似文献   

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