multivariate interpolation 中文意思是什麼
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The interpolation of scattered data by multivariate splines is an important topic in computational geometry
利用多元樣條函數進行散亂數據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 )
本質上，解決多元樣條函數空間的插值結點的適定性問題關鍵在於研究分片代數曲線，在高維空間里就是研究分片代數簇。 -
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
基於上述結果，提出了h - d空間散亂數據超曲面構造二步法，第一步應用局部最小二乘法或局部徑向基函數擬合法插補立方體網格點上的函數值，第二步應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。 -
Based upon practical engineering applications, the variant separating - variable algorithms of hyper - surface fitting for arbitrary multivariate scattered data are presented by separating positional variables in a spatial domain from certain physical variables such as time, mach number, angle of attack and so on, followed by their comparison. when compared with existing scatted data interpolation algorithms, the new ones are more effective. a sufficient condition to exchangeable order of separation is obtained and order of continuity on the hyper - surfaces above is discussed
三、以實際工程應用為背景，將具有某種物理意義的量（如時間、 ma數、迎角等）與空間位置變量分開處理，給出任意散亂數據超曲面擬合變量分離的各種演算法，對它們進行了演算法的分析比較，獲得了分離次序可交換性的充分條件，給出了變量分離法構造的超曲面的光滑階。
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