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directional derivative 【數學】方向導數。

directional gyro

Let / be a function from rn to r . following the definitions of the generalized gradients proposed by clarke and xu yihong , respectively , we define the d - regular weak lipschitz function and propose a new generalized gradient as follows where d _ f ( x ; d ) is the directional derivative of / in the direction d at the point x , namely some properties are proposed 第二節引入基本定義和記號,在clarke和徐義紅提出的各自的廣義梯度的基礎上,定義了一類d正則弱l函數,且提出了一個新的廣義梯度。設f : r ~ n r ,其廣義梯度為其中為f在處沿方向d的方向導數,即并給出了若干性質定理。

Finally , this thesis discussed these following questions : first , the algorithm of used the error image for improving the purpose of the edge detection . secondly , we have transformed the solved question of the first and the second directional derivative to frequency domain and founded they have a single formulae in frequency domain . thirdly , we have described the singular signal and the noise by using the correlations of the neighbor data after wavelet transform 最后,在傳統的邊緣檢測算法和小波分析的邊緣檢測算法之外,對以下幾個方面也進行了一些討論: 1 )利用誤差圖像來提高邊緣檢測效果的算法; 2 )將求解任意方向的一階、二階方向導數的問題轉換到頻域中去求解,發現在頻域中它們具有簡單易用的公式,使得原來求解任意方向的一階、二階導數的比較困難的問題變得容易實現了。

Section 3 and section 4 are the main parts of the paper . by employing the directional derivative and generalized gradient in the broad sense , as defined in this paper , the first order necessary condition and the first order sufficient condition of the single - objective non - smooth programming where the objective function is d - regular weak lipschitz function and constrained functions are regular weak lipschitz functions 第三節和第四節是本文的主要章節,以本文定義的廣義方向導數和廣義梯度為分析工具,對目標函數為d正則弱l函數,約束函數為正則弱l函數的單目標非光滑規劃分別給出了一階必要條件和一階充分條件。

Used perturbed method and making inexact generalized gradient projection with cone , perturbed generalized gradient projection method is proposed . the field of the algorithm is extended . numerical experiments show that the method is effective . secondly , using the trust region form and the pseudo - directional derivative of minimax problem , we propose the trust region form of minimax problem 對信賴域法作了進一步的研究,借助minimax問題的偽方向導數,構造出其信賴域二次模型,并結合非單調策略,給出求解minimax問題的簡單易行的信賴域算法。

As the directional derivative defined in this paper does n ' t show convexity , when its properties are considered , it is necessary to search for new ways to reach the conclusion 本文定義的廣義方向導數在一般情況下不具有凸性,因而研究其性質時,要采用新的方法來得到類似的結論。

Secondly , the new generalized gradient is introduced to take advantage of the given directional derivative 其次討論了一類新的廣義梯度,這樣的廣義梯度能夠充分利用已經有的方向導數的信息。

We discuss several different definitions of directional derivative and gradient vector 摘要討論了幾種不同的方向導數和梯度的定義。

Error estimates of directional derivatives of approximately specified functions 近似已知函數方向導數的誤差估計

Derivatives in higher dimensions , directional derivative and gradient 在多維度中的微分、方向導數和梯度。

Derivatives in higher dimensions , directional derivative and gradient 多維微分、方向導數和梯度。