The interpolation of scattered data by multivariate splines is an important topic in computational geometry 利用多元樣條函數(shù)進行散亂數(shù)據(jù)插值是計算幾何中一個非常重要的課題。
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 ) 本質(zhì)上,解決多元樣條函數(shù)空間的插值結(jié)點的適定性問題關(guān)鍵在于研究分片代數(shù)曲線,在高維空間里就是研究分片代數(shù)簇。
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 基于上述結(jié)果,提出了h - d空間散亂數(shù)據(jù)超曲面構(gòu)造二步法,第一步應(yīng)用局部最小二乘法或局部徑向基函數(shù)擬合法插補立方體網(wǎng)格點上的函數(shù)值,第二步應(yīng)用多元樣條光滑快速插值計算,使所得超曲面具有c ~ 1或c ~ 2連續(xù)。
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 該方法的意義是:推廣了雙三次coons曲面的理論與算法,并對邊界條件進行了簡化改進,可以直接由插值條件獲得邊界條件,從而克服了多元樣條邊界條件難以確定的困難,拓寬了應(yīng)用范圍。
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 鑒于基于隨機模擬技術(shù)的遺傳算法在求解隨機規(guī)劃問題上的優(yōu)越性,本文指出,改變遺傳算法的參數(shù)條件,在此基礎(chǔ)上求得機會約束規(guī)劃的若干個最優(yōu)值,以這些最優(yōu)值為樣本點,利用多元樣條回歸,擬合得到最優(yōu)值函數(shù),進而求出最優(yōu)值函數(shù)的lipschitzs常數(shù),從而對于任一機會約束規(guī)劃問題,都可以得到它的一個區(qū)間估計。