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本文首先利用由两组具有局部最小支集的样条所组成的基函数,构造非均匀2 型三角剖分上二元三次样条空间S31,2(Δmn(2))的若干样条拟插值算子. 这些变差缩减算子由样条函数Bij1支集上5 个网格点或中心和样条函数Bij2支集上5 个网格点处函数值定义. 这些样条拟插值算子具有较好的逼近性,甚至算子Vmn(f) 能保持近最优的三次多项式性. 然后利用连续模,分析样条拟插值算子Vmn(f)一致逼近于充分光滑的实函数. 最后推导误差估计. 相似文献
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In this paper we address the problem of constructing quasi-interpolants in the space of quadratic Powell-Sabin splines on
nonuniform triangulations. Quasi-interpolants of optimal approximation order are proposed and numerical tests are presented.
Dedicated to Prof. Mariano Gasca on the occasion of his 60th birthday. 相似文献
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Under mild additional assumptions this paper constructs quasi-interpolants in the form
with approximation order ℓ−1, whereh(x) is a linear combination of translatesψ(x−jh) of a functionψinCℓ(
). Thus the order of convergence of such operators can be pushed up to a limit that only depends on the smoothness of the functionψ. This approach can be generalized to the multivariate setting by using discrete convolutions with tensor products of odd-degreeB-splines. 相似文献
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In this article, we use a multilevel quartic spline quasi-interpolation scheme to solve the one-dimensional nonlinear Korteweg–de Vries (KdV) equation which exhibits a large number of physical phenomena. The presented scheme is obtained by using the second-order central divided difference of the spatial derivative to approximate the third-order spatial derivative, and the forward divided difference to approximate the temporal derivative, where the spatial derivative is approximated by the proposed quasi-interpolation operator. Compared to other numerical methods, the main advantages of our scheme are the higher accuracy and lower computational complexity. Meanwhile, the algorithm is very simple and easy to implement. Numerical experiments in this article also show that our scheme is feasible and valid. 相似文献
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The aim of this survey paper is to propose a new concept “generator”. In fact, generator is a single function that can generate
the basis as well as the whole function space. It is a more fundamental concept than basis. Various properties of generator
are also discussed. Moreover, a special generator named multiquadric function is introduced. Based on the multiquadric generator,
the multiquadric quasi-interpolation scheme is constructed, and furthermore, the properties of this kind of quasi-interpolation
are discussed to show its better capacity and stability in approximating the high order derivatives. 相似文献
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Li Zha Renzhong Feng~* 《高等学校计算数学学报(英文版)》2007,16(4):348-357
In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function.In particular,for twicely differ- entiable function the proposed method provides better approximation and also takes care of derivatives approximation. 相似文献
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The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function to scattered data quasi-interpolation. It is shown that high order approximation of smooth functions up to some prescribed accuracy is possible, if the basis functions, which are centered at the scattered nodes, are multiplied by suitable polynomials such that their sum is an approximate partition of unity. For Gaussian functions we propose a method to construct the approximate partition of unity and describe an application of the new quasi-interpolation approach to the cubature of multi-dimensional integral operators. 相似文献
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Quasi-interpolation is very useful in the study of approximation theory and its applications,since it can yield solutions directly without the need to solve any linear system of equations.Based on the good performance,Chen and Wu presented a kind of multiquadric (MQ) quasi-interpolation,which is generalized from the L D operator,and used it to solve hyperbolic conservation laws and Burgers’ equation.In this paper,a numerical scheme is presented based on Chen and Wu’s method for solving the Korteweg-de Vries (KdV) equation.The presented scheme is obtained by using the second-order central divided difference of the spatial derivative to approximate the third-order spatial derivative,and the forward divided difference to approximate the temporal derivative,where the spatial derivative is approximated by the derivative of the generalized L D quasi-interpolation operator.The algorithm is very simple and easy to implement and the numerical experiments show that it is feasible and valid. 相似文献
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一类二次保形拟插值函数的研究 总被引:1,自引:0,他引:1
通过讨论一种保形拟插值的基函数与二次规范B-样条函数之间的关系,提出了一类二次保形拟插值样条函数,得到了这类保形拟插值函数在具有线性再生性质,并保持原有数据点列的单调性和凸性时分别应满足的条件,并给出几个应用实例. 相似文献