查询词典 projection gradient method

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。

Psychophysical experiments were carried out using both single stimulus method based on random-gradient method and one-interval-forced-choice method.

采用的心理物理学实验方法是单刺激随机阶梯法和单择一强迫选择法。

Based on analysis and comparison of the principle, method and form of train mass calculation and the correlative" select-judge value" for raising speed train,a change of particular attention from train mass to train speed is recommended in this paper,and the second critical gradient between the recommendatory maximum speed method and the traditional calculative speed method is established to the "select-judge value".

本文在分析与比较提速列车质量计算的原则和方式方法以及相关的选择判别值的基础上，提出应从传统的侧重列车质量的方式转向侧重运行速度的方式，并最终确立第二临界坡度为推荐的最高速度法与传统的计算速度法的选择判别值。

So it can be avoided that the computation accuracy is lowered and the calculation result is hard to be convergent for the odd state of transformation matrix.The computation accuracy of wavelet Ritz method and wavelet Galerkin method has been improved so the special'microscopic'property could be fully expressed. An effective method is offered also to solve the problem of high stress gradient and some other odd state problems in engineering.

从而避免了由于转换矩阵奇异而造成精度下降且计算结果不易收敛的问题，提升了小波Ritz法和小波Galerkin法的求解精度，使小波分析的"显微"特性得以充分发挥，并为应力大梯度问题和工程奇异问题的有效求解提供了强有力的计算手段。

The mixed method raise the convergent rate of the conjugate gradient method, and solve the problem which the steepest descent method can not solve in the condition with badly characteristics for the objective function.

混合算法既提高了共轭梯度算法的收敛速度，又解决了目标函数"性态不优"时，最速下降法难以求解的问题。

To solve the three-dimensional (3-D) weak-form volume electric field integral equation, there is a traditional method named Generalized Minimum Residual Method except the conjugate gradient method.

对于三维(3-D)弱形式的电场体积分方程，除了共轭梯度方法，另一种广泛采用的方法便是广义最小余量方法。

With the guide of non-linear program theory, by using interpolative steps and inexact line search, an improved conjugate gradient method was found, by which the training rate of BP networks increases by tens or hundreds of times. Moreover, the improved method is effective to solve non-linear equations for which Newton's method does not converge owing to the problems of the quadratic derivative and inverse matrix.

通过大量的数值模拟试验发现，在非线性规划理论的指导下采用间插步骤和不精确的一维搜索技术改进的共轭梯度法，是基于梯度和共轭方向的连续搜索算法中最有效的算法，这种算法使BP网络的训练速度提高几十到几百倍，使BP网络的实际应用效果大为改善；而且这种算法对于用牛顿法由于求二阶导数和求逆矩阵等问题难于收敛的非线性方程组的求解也是很有效的。

Fast marching method is a fast, accurate and stable traveltime computation method. This method is flexible, fast, and unconditionally stable for arbitrarily large gradient jump in velocity.

波前快速推进法是一种快速、准确而稳定的走时计算方法，它不仅计算速度快、灵活性好，而且对任何复杂速度场都具有无条件稳定的特点。

This dissertation gives the damping iteration method and geome-tric-mean tracing method, both based on inversion of observed ground-water level data, and also gives the proportional iteration (or ortho-gonalization) method based on inversion of hydrogeologic gradient data.

本文建立了用水位观测资料进行反演的阻尼迭代法和几何均值追踪法，利用水力梯度资料进行反演的比例迭代法。

An equal cross-section blade was investigated and a finite element model was built parametrically. Geometrical parameters (such as length, width and thickness), material parameters (such as young's modulus and density) and speed of blade were considered as input random variables while the static frequencies and dynamic frequencies were output random variables. Combining the finite element method, response surface method and Monte Carlo method, the statistical properties and cumulative distribution functions of static frequencies and dynamic frequencies were obtained. Probability sensitivities analysis, which combined the slope of the gradient and the width of the scatter range of the random input variables, was applied to quantitatively evaluate the sensitivities of static frequencies and dynamic frequencies with respect to the random variables. The Scatter plots of structural responses with respect to the random input variables were illustrated how to adjust the values of the static frequencies and dynamic frequencies by changing input random variables.

文中以某试验台用汽轮机等直叶片为研究对象，考虑几何参数、材料参数和转速的随机性，通过有限元参数化建模，将确定性有限元方法、响应面方法和Monte-Carlo模拟法相结合，从而获得了叶片静频、动频的统计特性和累积分布函数；同时考虑随机变量的梯度和离散范围对静、动频的影响，通过概率敏感性分析，定量地判断出叶片静、动频对随机输入变量的敏感性；通过绘制叶片静、动频与输入变量的散点图，定量地分析了如何改变随机变量以调整静、动频率的方法。

We were cousins—his grandfather was King of Scots,and his great-grandfather was Henry VII of England.

我们是堂姐弟——他的祖父曾是苏格兰国王，他的曾祖父是英格兰的亨利二世。

I do want to help you, but I am in a quandary now!

我是想帮你，但是我现在左右为难啊！