| 1. | The interpolation of scattered data by multivariate splines is an important topic in computational geometry
利用多元样条函数进行散乱数据插值是计算几何中一个非常重要的课题。 |
| 2. | Essentially , a key problem on the interpolation by multivariate splines is to study the piecewise algebraic curve and the piecewise algebraic variety for n - dimensional space rn ( n > 2 )
本质上，解决多元样条函数空间的插值结点的适定性问题关键在于研究分片代数曲线，在高维空间里就是研究分片代数簇。 |
| 3. | Two - stage - fitting ( tsf ) method is obtained , which consists of evaluating the function values of regular - grid points by using local weighted least square methods or radial function interpolation , and smoothly and quickly interpolating those points by using multivariate splines . the result is a hyper - surface of c1 or c : continuity
基于上述结果，提出了h - d空间散乱数据超曲面构造二步法，第一步应用局部最小二乘法或局部径向基函数拟合法插补立方体网格点上的函数值，第二步应用多元样条光滑快速插值计算，使所得超曲面具有c ~ 1或c ~ 2连续。 |
| 4. | The significance established the system is to generalize the theories and methods of bi - cubic coons surfaces and to simplify the boundary conditions greatly which can are directly derived from the given interpolating data . hence the difficulty of determining boundary conditions of multivariate spline is overcome , which makes it use in many applications . 2
该方法的意义是：推广了双三次coons曲面的理论与算法，并对边界条件进行了简化改进，可以直接由插值条件获得边界条件，从而克服了多元样条边界条件难以确定的困难，拓宽了应用范围。 |
| 5. | In view of the fact that the genetic algorithm of stochastic programming based on random simulated technology has succeed greatly , this paper points out that changing parameters of genetic algorithm can obtain a sequence of optimum values of goal function . taking these genetic algorithm values as sampling data , we can get fitting optimum function by using multivariate spline regression and get the lipschitzs constant of the fitting optimum function . so for any chance constrained programming problem , we can get its interval estimate
鉴于基于随机模拟技术的遗传算法在求解随机规划问题上的优越性，本文指出，改变遗传算法的参数条件，在此基础上求得机会约束规划的若干个最优值，以这些最优值为样本点，利用多元样条回归，拟合得到最优值函数，进而求出最优值函数的lipschitzs常数，从而对于任一机会约束规划问题，都可以得到它的一个区间估计。 |
| 6. | The piecewise algebraic curve and the piecewise algebraic variety , as the set of zeros of a bivariate spline function and the set of all common zeros of multivariate splines respectively , are new and important concepts in algebraic geometry and computational geometry . it is obvious that the piecewise algebraic curve ( variety ) is a kind of generalization of the classical algebraic curve ( variety respectively )
分片代数曲线作为二元样条函数的零点集合，分片代数簇作为一些多元样条函数的公共零点集合，它们是代数几何与计算几何中一种新的重要概念，显然也是经典代数曲线与代数簇的推广。 |
