插值多项式

Comparing to the algebraic polynomial,the trigonometric polynomial interpolation studying is more difficult ,and the methods are more different.

与代数多项式相比，三角多项式插值的研究要困难一些，研究方法也有众多不同。

The parametric speed of the curve is firstly approximated by the Bernstein polynomial, which takes the lengths of control point vectors of the direction curve of normal as Bézier coordinates.

其次 ，基于参数速度的 L egendre多项式逼近和插值区间端点的 Jacobi多项式逼近，导出了保持法矢平移方向的两种代数方式的等距有理逼近算法。

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 this paper, We firstly present a nonuniform sampling DCT method based on the relationship of Chebyshev polynomial interpolation and DCT, in which, the sampling points are chosen as zeros of Nth degree Chebyshev polynomials of the first kind.

文章首先利用Chebyshev多项式插值与DCT变换之间的相互关系，提出了基于第一类Chebyshev多项式的第N次多项式的零点作为非均匀取样点的DCT变换方法。

The problems are investigated by using polynomial interpolation and symbolic computation, and the proposed method is applied for curve and surface cases.

基于多项式插值和符号计算的思想，研究了Bernstein多项式函数复合问题，并将其应用于曲线曲面的情形。

Based on polynomial interpolation and approximation theory,a Chebyshev orthogonal basis neural network is constructed in this paper.

根据多项式插值和逼近理论构造一个切比雪夫正交基神经网络，其模型采用三层结构并以一组切比雪夫正交多项式函数作为隐层神经元的激励函数。

In this paper, the Lagrange interpolation formula asked a class function expression question, the determination function to the higher mathematics in the elementary mathematics in some value scope question, the equality proof question, the multinomial factorisation question, to ask to have the Finite series to pass the formula question, the certificate any n function at will n+1 different spots function value maximum value minimal problem and so on six aspects should serve as the simple introduction, and has separately made the comparison with these six aspects elementary mathematics method, thus solved some operation problems in elementary mathematics.

摘要本文对高等数学中Lagrange插值公式在初等数学中的求一类函数表达式问题、确定函数在某点的取值范围问题、恒等式的证明问题、多项式的因式分解问题、求有穷数列的通项公式问题、证明任一n次函数的随意的n+1个两两不同点的函数值的最大值的最小值问题等六个方面的应用作了简单介绍，并与这六个方面的初等数学方法分别作了比较，从而解决一些初等数学中的运算问题。

First, orthogonal circle operator was modeled in terms of Zernike orthogonal complex moment; the one-to-one mapping between the edge point and the parameters of the circle was established by the algorithm. Then, quadratic polynomial interpolation was adopted to further locate the edge points in the gradient direction.

首先根据Zernike正交复数矩建立圆物体边缘点与边缘参数之间的映射关系，并提取边缘点；然后利用二次多项式插值在梯度方向上对提取出的边缘点进行进一步定位；最后利用最小二乘法拟合插值后的边缘点，得到亚像素精度的圆参数。

In this paper,the rational approximation of the offset curve of Bézier curves is obtained when a polynomial of symmetric power basis is used to approximate the norm of parametric speed of Bézier curves.

等距曲线逼近技术的关键在于参数速度的逼近，文章用S幂基多项式逼近平面Bézier多项式曲线的参数速度模长，得到Bézier多项式曲线的等距曲线的有理逼近曲线，所得有理多项式逼近曲线与等距曲线在端点处能够达到高阶插值。

The rational finite element formulates directly in the physical domain and interpolates with the solutions, rather than using the iso parametric technique and interpolates with polynomials in the computational plane.

理性元直接在物理面内列式，并用微分方程的解插值，不用等参技术而在计算面内用多项式插值。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐