梯度法

In allusion to the defect of grads descension of traditional back propagation network algorithms, some improving measures such as adaptive learning and additive momentum has been taken, and better application result is acquired.

针对基于梯度下降法的BP网络存在的学习效率低、收敛速度慢、易陷于局部极小状态、网络的泛化及适应能力较差等缺陷，采用了附加动量法及自适应学习率、合理选择激励函数等策略对算法中的缺陷给出了改进措施，取得了较好的应用效果。

So based on the characteristics of gradient descent method and layer by layer optimization method, we made some modifications and improvements on both of them.

本文就是针对梯度下降法和逐层优化法的特点，在现有算法的基础上，做了一些改进和修正。

Two ways are used to design the network,the one is the direct energy descent method,and the other is the gradient descent method .

有两种方法可以用来设计网络，一是能量下降法，另一个是梯度下降法。

Thirdly, in order to improve the learning efficiency and stability of feedforward neural network, a fast learning algorithm for neural networks based on CGM-OC approach is presented. Compared with other learning methods such as BP method, Broyden Flecher Goldfarl Shanno method and Powell method in which the derivative is replaced by the difference quotient etc, simulation results show that the proposed method is an efficient and fast one.

第三，为了提高前馈神经网络权值的学习效率及稳定性，提出一种基于正交校正共轭梯度优化方法的神经网络学习算法，通过与其它学习算法（如：BP算法、变尺度法、用差商近似代替导数的Powell法等）的比较，经仿真试验表明，本算法是一种高效、快速的学习算法。

Base on the mathematical equation: the quantity of conduction heat flex is equal to the product of heat conduction coefficient and gradient of temperature, we expect to obtain the result which is better than that of Transient Hot-wire Method and Steady-State Parallel-Plate Method, and simplify the strategy of measurement.

理论模式关系中，使用热传量等於热传系数与温度梯度乘积的比例关系式作为理论基础，目的在得到更优於暂态热金属线法(Transient Hot-wire Method)及稳态平行板法(Steady-State Parallel-Plate Method)的量测结果，同时也简化了量测方式。

In order to analyse the structural reliability by stochastic finite element method rapidly and efficiently, a method combined with finite element method and gradient optimum algorithm based on ANSYS is presented when referring to the geometric interpretation of structural reliability index.

为快速、高效地进行基于随机有限元法的结构可靠度分析，从结构可靠性指标的几何意义出发，提出了在ANSYS平台上采用有限元法和梯度优化算法相结合的方法进行可靠度分析的构想，对ANSYS进行二次开发实现了该方法。

In Chapter 4, a symmetric triangular partitioned secant method for solving large scale sparse unconstrained optimization problems is constructed, which is a combination of a secant method and a finite difference method, and depends on a consistent partition of the columns of the lower triangular part of the Hessian matrix; it reduces the number of gradient evaluations required by Powell and Toints algorithm (the indirect lower triangular substitution algorithm) by one at every iterative step.

此算法是基于稀疏Hesse阵的下三角部分的列的相容分划的基础上建立起来的，把割线法和有限差分法有机的结合在了一起，在每次迭代中，把由Powell和Toint的算法所需要的梯度赋值次数减少了一。

First, we extract the boundaries between two different materials by weighting with gray-level gradient,and only voxels on these boundaries participate in the generation of each image, so it drastically reduces the rendering time. Second. We think the voxels on boundaries as the mixture of different materials,so in every voxel there is a surface. We use the oriented cube-interpolation technique to get the intersection point of viewing orientation and the surface in the voxel, then compute the surface normal of the intersection point. We use the normal to shade the voxel in order to improve the image quality.

首先，采用灰度梯度加权提取出三维数据场中不同物质间的边界，根据显示的需要只对这些边界上的体元赋予相应的阻光度并进行光亮度合成计算，因而可大大减少计算量，提高显示的速度；将边界上的体元作为不同物质的混合体，采用与方向有关的三线性插值来计算视线方向与体素内等值面的交点，根据交点的法向量进行光照效应计算以提高显示图像的质量；最后用投影成像法显示最终的图像。

The eleven point curvature-computing method is used to locate the area of corner and point of tangency.

采用最大方差法将图像二值化，用图像形态学的梯度细化和修剪算法来提取边缘轮廓，利用十一点曲率法得到轮廓的角点和切点的大致位置。

For the optimization of the continuous variables, the author combines the weaken idea, the DFP and the gradient projection method to form a modified Goldfarb method by which the optimal problems of the trusses can be solved.

对于连续变量优化，作者将松弛思想、变尺度公式和梯度投影法相结合，建立了一种专门解决杆系优化问题的修正Goldfarb法，算例计算表明本法是针对性强、效率高的优化算法。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。