| 1. | Derivatives in higher dimensions , directional derivative and gradient
多维微分、方向导数和梯度。 |
| 2. | Derivatives in higher dimensions , directional derivative and gradient
在多维度中的微分、方向导数和梯度。 |
| 3. | Error estimates of directional derivatives of approximately specified functions
近似已知函数方向导数的误差估计 |
| 4. | We discuss several different definitions of directional derivative and gradient vector
摘要讨论了几种不同的方向导数和梯度的定义。 |
| 5. | Secondly , the new generalized gradient is introduced to take advantage of the given directional derivative
其次讨论了一类新的广义梯度，这样的广义梯度能够充分利用已经有的方向导数的信息。 |
| 6. | Next , in the interior of the patches , surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing virtual iso - parametric curves
其次，在曲面片内部，曲面拟合点和边界方向导数可以从参考曲线中通过构建虚拟等参线的方法得到。 |
| 7. | 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
本文定义的广义方向导数在一般情况下不具有凸性，因而研究其性质时，要采用新的方法来得到类似的结论。 |
| 8. | 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
对信赖域法作了进一步的研究，借助minimax问题的伪方向导数，构造出其信赖域二次模型，并结合非单调策略，给出求解minimax问题的简单易行的信赖域算法。 |
| 9. | 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
第三节和第四节是本文的主要章节，以本文定义的广义方向导数和广义梯度为分析工具，对目标函数为d正则弱l函数，约束函数为正则弱l函数的单目标非光滑规划分别给出了一阶必要条件和一阶充分条件。 |
| 10. | 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，在传统的边缘检测算法和小波分析的边缘检测算法之外，对以下几个方面也进行了一些讨论： 1 )利用误差图像来提高边缘检测效果的算法； 2 )将求解任意方向的一阶、二阶方向导数的问题转换到频域中去求解，发现在频域中它们具有简单易用的公式，使得原来求解任意方向的一阶、二阶导数的比较困难的问题变得容易实现了。 |
