查询词典 interpolation formula

In this paper,some problems on bivariate Hermite interpolation by polynomial are studied.The concepts of strong H-basis and Hermite interpolation along a plane algebraic curve are proposed.

1引言如所知，光滑函数方法被广泛地应用于计算机辅助几何设计，有限元及散乱数据插值与拟合(Scattered data fitting and interpolation)等领域·在应用该方法过程中，有关光滑或Hermite插值格式及其显式表达式问题的研究是至关重要的一个方面。

If the complex or irregular contour parts is machined in the CNC machine only with straight lines, arcs and other simple analytic curve interpolation function, it need to adopt off-line interpolation method.

采用只具有直线、圆弧等简单解析曲线插补功能的CNC机床加工复杂或不规则的零件轮廓，需要采用离线插补的方法。

We investigate mainly solving the hyperbolic and parabolic equations by using the MQ quasi-interpolation. The underlying idea of our means is that: employing the derivative of the MQ quasi-interpolation to approximate the spatial derivative of the PDE, while the approach of the temporal derivative of the PDE is used a finite difference.

我们主要就MQ拟插值在双曲型方程和抛物型方程中的应用进行了研究，其基本思路是：利用MQ拟插值的导数逼近微分方程的空间导数，而微分方程的时间导数则采用有限差分逼近。

In this dissertation, the following critical theoretical problems on local La-grangian numerical differentiation are studied: explicit formulas, local estimate for the remainder, and the highest order of approximation in the case that the values of the function at these interpolation nodes have perturbationsLagrangian numerical differentiation is a method that the Lagrange interpolation polynomialis differentiated to approximate the derivative, where Tn ={t_0,t_1,......

本文主要研究有关局部Lagrange数值微分法的一些关键性的理论问题：公式的显式表示，余项的渐近估计，以及在插值数据有扰动的情况下，局部Lagrange数值微分法的最大逼近阶。

The arc data interpolation error by secant, tangent and chord, and the smallest error by secant mode is analyzed in this paper. The relation between the maximum radial error and arc radius and approach step-length in the secant mode of arc data interpolation in CNC system is detailed.

在分析数控系统圆弧数据插补割线方式较切线、内接弦插补方式误差更小的基础上，讨论了数控系统圆弧数据插补割线方式中最大径向误差与圆弧半径和逼近步长的关系。

The development of polygonal finite elements is discussed, including Wachspress interpolation, Laplace interpolation and barycentric coordinates.

论述了多边形有限元的发展历史，给出了多边形单元上的Wachspress插值、Laplace插值和重心坐标的一些最新研究成果。

Approximating unknown function by barycentric Lagrange interpolation which has advantages of higher precision and good numerical stability, the barycentric interpolation collocation method for analyzing deformation and buckling load of ring is presented.

采用数值稳定性好、计算精度高的重心Lagrange插值近似未知函数，提出数值分析圆环变形和临界载荷的重心插值配点法。

In theory of approximations, the classic methods of polynomial approximation for rational expression are various interpolations and operator approximations, such as Lagrange interpolation, Hermite interpolation and Bernstein polynomial approximation.

在逼近论中，用多项式逼近有理式的经典的方法是各种插值与算子逼近方法，如Lagrange插值、Hermite插值和Bernstein多项式逼近等。

The basic idea is as follows: first, a kind of plane α-B-spline interpolation curve with a shape control parameter a is constructed; then, by converting the first derivatives of the curve into Bernstein polynomial, the positive conditions of Bernstein polynomial can be used to get the necessary and sufficie nt conditions for the monotonicity of α-B-spline interpolation curves, i.e., the range of the parameter a. Therefore, monotone-preserving interpolating curves can be obtained succinctly.

其基本思想是：首先构造带有形状可调参数的一类平面(-B样条插值曲线，再把其一阶导矢的两个分量分别转化为Bernstein多项式，从而利用Bernstein多项式的正性条件，得到此曲线为单调的充要条件，即形状参数的取值范围，简单、快捷地实现此参数样条曲线的保单调插值。

For the given endpoint interpolation conditions, a new approximation method of multidegree reduction is presented. Using Chebyshev polynomial approximation theory, the nearly best uniform approximation under the interpolation conditions of endpoints can be obtained.

对于给定的首末端点的各阶插值条件，给出了一种新的一次降多阶逼近算法，应用Chebyshev多项式逼近理论达到了满足端点插值条件下的近似最佳一致逼近。

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。