approximation by least squares 中文意思是什麼

approximation by least squares 解釋
用最小二乘方的近似法
  • approximation : n. 1. 接近；近似。2. 【數學】近似值。3. 概算，略計。
  • by : adv 1 在側，在旁，在附近。2 （擱）在一邊，（放）到旁邊，（存）在一旁；收著。3 （由旁邊）經過，過...
  • least : adj （little 的最高級，比較級為 less 或 lesser）1 最小的，最少的 （opp most）。2 最不重要的，地位...
  • squares : 方鋼
  1. At first, this paper analyzes the factors of water - sand influencing water level of yellow river and the feasibility just using the factors of water - sand to study water level, and collects the corresponding data ; secondly, because there are strong nonlinear relation in the corresponding data, by meticulous theory analysis, this paper integrates basic nonlinear analysis method, theory of random analysis, method of least squares and so on. it puts forward a method which can get the high accuracy simulation of the data, perfects the multi - factor analysis of variable ( over three factors ) of the statistic ; thirdly, it applies the method to the approximation of corresponding water level process which belong to the capacity of sand of middle - high and middle - low, and get the high - accuracy simulation about the typical nonlinear relation ; at last, this paper definitudes the main influence mode that the capacity of sand. it mainly unite with other factors to work on the water level in the yellow river lower reaches ; mor eover, this paper analyzes the difficult point and the direction of improvement to realize the accuracy forecasting of the flood level of erodible - bed channel

    首先，系統分析了影響黃河水位的水沙因素，及僅用水沙因素有效研究水位的可行性，並按變量對應思想採集它們的相應數據；其次，由於相應水位過程數據中含極強的非線性關系，本論文經細致的理論分析，將基本的非線性分析方法、統計建模方法、隨機分析理論、最小均方誤差原則等等數學理論及方法有機揉合，提出了能有效實現這類數據高精度擬合的分層篩選法，並改進了統計學中多因子（三個以上）方差分析法；再次，將這一方法用於黃河中高及中低含沙類洪水相應水位過程的擬合，實現了這一典型非線性關系的高精度擬合，各年汛期上下游相應洪水位過程的擬合誤差都較小；最後，明確黃河下游含沙量對水位的主要影響方式，即含沙量主要是與其它因素聯合對水位作用；另外分析了要實現變動河床洪水位過程準確預報的困難所在及改進方向。
  2. The new algorithm starts from an initial estimate which is based on the hough transform, and a rectangular window is centered using the current line approximation, and a new line estimation is generated by making a total least squares fit through the pixels contained within the window. this is repeated until convergence is reached. lastly, we have suggested a new technique which may recover the motion and structure parameters of a moving object by using of 21 optical flow lines based on the optical flow fields of the feature line this thesis is the project supported by aeronautical foundation science ( no. 99f53065 ) and research center of measuring and testing technologies, and control engineering in nanchang institute of aeronautical technology ( no. 2001 - 15 )

    演算法的思路是：首先，在小區域內運用霍夫變換確定直線的初始值；其次，以直線的初始值所對應的直線為中心線，建立一個矩形框；最後，利用矩形框內所包含的邊緣點數據不斷地迭代直至收斂，從而達到進一步修正直線的坐標參數；本文基於特徵直線的光流場，即線流場，建立了一種利用21條光流線確定空間三維物體旋轉運動參數、平移運動參數以及對應的空間直線坐標的線性演算法。
  3. For h - d scattered data, local weighted least - squares fitting ( llsf ) methods for approximation and interpolation are respectively put forward and the latter is got by adjusting weight function in the former case, and the interpolating method is also used to construct hyper - surface models with the radial function. the problem of choosing weight function during local least square approximation is discussed and two good weight functions are given : one with a parameter, the other with no parameter. based on them

    二、對非規則區域上分佈的h - d數據，提出了散亂數據超曲面擬合的局部最小二乘逼近法。通過對局部最小二乘逼近的權因子作適當的改進，得到了擬合精度較高的局部最小二乘插值法，還用徑向基函數構造了超曲面模型，找到了一種性質好帶參數的權函數以及另一種有著普遍精度性質的不含參數的權函數，獲得了較好的逼近效果。
  4. Lbie, based on the local boundary equation, adopts the traditional moving least squares ( mls ) approximation which depends on only the values of the nodes in the domain of the problem or along its boundary. the whole process of integration is carried on over a local domain or its local boundary centered at the node in question. the local boundary equation can be rewritten to represent the values of the unknown function at the point of interest, and the essential boundary conditions can be directly and easily enforced by using the green formula and the characters of the dirac function

    它以局部邊界積分方程為基礎，採用移動最小二乘近似函數，從而只需要分佈在問題域內及其邊界上的節點的信息值，無需劃分單元；整個積分是在以節點為中心的局部域及其邊界上實現，所以不需要背景積分網格；藉助于格林公式及dirac函數的性質，將局部邊界積分方程轉化為所考慮點的未知函數的邊界積分表達式，便於直接施加本質邊界條件。
  5. By using the universal approximation property of neural networks ( nn ), a three - layer feedforward neural networks is embedded into the framework of standard pls ( partial least squares ) modeling method resulting in a nonlinear pls - nn model

    提出將線性pls模型通過神經網路逼近策略拓展到非線性的pls - nn方法，構造了基於梯度下降演算法的神經網路權值矩陣學習規則。
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