查询词典 interpolation of operators

In chapter 4, a family of two-parameter operators on Abelian group is introduced and its interpolation theorem for approximation is established.

所得的结果包含了R.DeVore定理作为特款，还包含了算子逼近的插补定理，是非线性逼近方面的一项基础性工作。

This is an untouched measuring way. The cameras are calibrated in the way of RAC two steps, first. With the polynomial interpolation, the pictures catched from the steel plate are treated to detect the edge in subpixel with a cross window arithmetic operators, which can fit non uniform illumination, keep the edge character and do filter in a better way. Three-dimensional scenery could be rebuilt from the two-dimensional pictures with the methods of least square fitting and contradictorily clairvoyance. Thus, the distance and its variance of two points in the given position of the plate can be achieved. It is expected that this study can provide a new and useful tool to the research on the theory of distortion of line heating.

这种非接触的测量方式，采用RAC两步法对摄像机进行标定，然后对采集到的钢板图像进行分析处理，通过多项式插值的方法，采用具有保持边缘特征和滤波功能，且能适应非均匀照明的十字窗图像边缘检测算子进行象素级边缘检测，再用最小二乘拟合法和逆透视法对二维图像进行三维重建，便可测出钢板上给定点的距离及其变化值，以期为水火弯板的变形机理研究提供一种新的检测手段。

As to how to avoid weaknesses of these two operators, scholars have made unremitting efforts. One of the most famous is the French mathematician Sablonniere P, who introduced and studied a kind of new quasi-Bernstein interpolation operators in 1992. This kind of operators have given dual attention to the Lagrange operator and the Bernstein operator merit, and have avoided the twos deficiency.

对于这两种算子如何扬长避短，学者们做了不懈努力，其中最为著名的是法国数学家Sablonniere P，他于1992年引入并研究了一种新的拟Bernstein插值算子B上标(k 下标 n，，这是一类介于Lagrange算子与Bernstein算子之间的拟插值算子，这类算子兼顾了Lagrange算子与Bernstein算子的优点，克服了二者的不足。

Therefore,we know that under the mean of statistics, interpolation operators are not only ideal algorithm for realizing optimal approximation polynomials computation,but also ideal computing tool for realizing optimal information- based operation,and the property of their recover functions are good.

这说明了在统计学意义下，插值多项式算子一方面是实现最佳逼近多项式计算的理想算法，另一方面(来源：ABCdd论文网www.abclunwen.com)是实现最优信息基算法的理想计算工具，且具有性质优良的恢复函数。来源：AB03c303C论文网www.abclunwen.com

The main content includes that the accuracy of interpolation operators is creased since defect equations introduce less error: Gauss-Seidel solution can save effectively the computational time, in particular, the CPU-time for the setup phase; Jacobi-relaxation interpolation contributes to efficient and robust algebraic multigrid methods by a simple and purely algebraic mean.

最主要的内容是基于亏量方程引入的误差较小，从而进一步提高插值算子的精度；采用Gauss-Seidel解法有利于节省计算时间，特别是预备阶段的CPU时间；插值的松驰以一种简单的纯代数的方式获得高效且稳健的代数多重网格算法。

Fourthly,in the UMD spaces,the tree martingale transforms and their maximaloperators are defined,and then based on the geometrical property of UMD spaces andcombining new interpolation techniques of Hardy-Lorentz spaces,the inequality ofUMD space valued tree martingale transform maximal operators is obtained.

然后，在UMD空间中，我们定义了树鞅鞅变换及其极大算子，并用UMD空间几何性质和Hardy-Lorentz空间的算子插值理论证明了UMD空间值树鞅鞅变换的极大算子不等式。

From our results we know that the average error of the Lagrange interpolation sequence and the Hermite interpolation sequence based on the Chebyshev nodes in the 1-fold integrated Wiener space equal weakly to the average error of their corresponding optimal approximation polynomial in the 1-fold integrated Wiener space,and as a kind of information-based operation,they have simple form and their recover functions are polynomials,in the 1-fold integrated wiener space,their average error equal weakly to the corresponding minimal information radius whose permissible information operators class is function values.

通过我们的结果可以知道，基于第一类Chebyshev多项式零点的Lagrange插值算子列和Hermite插值算子列在1-重积分Wiener空间下的平均误差弱等价于相应的最佳逼近多项式在1-重积分Wiener空间下的平均误差，并且作为形式简单且恢复函数为多项式的一种信息基算法，其在1-重积分Wiener空间下的平均误差弱等价于相应的以函数值计算为可允许信息算子的最小平均信息半径。

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