查询词典 gradient method

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。

In the light of the complex, high-level and non-linear feature of the mathematical model which describe the transport of the coalbed methane, this paper study the fully-implicit solving method of the mathematical model in detail. Based on the complexity of the algebraic equations which are formed eventually, according to the alternating direction implicit difference pattern, this paper use the iterative method and the fully main element Gauss-Jordan eliminating method to solve equations, which is to use the iterative method to determine coefficient matrix and use the fully main element Gauss-Jordan method to solve th linear algebraic equation group, at the same time of studying the solving method of the mathematical model, according to the devising requirement of FORTRAN77 program structure, this paper draw up computer program and form the corresponding computer model, and verify the validity and reliability of the model in theory by operating the model.

重点研究了模型内、外边界及有关参数的处理，针对描述煤层甲烷运移的数学模型是一个复杂、高阶非线性数学模型的特点，详细研究了模型的全隐式求解方法，根据最后形成的代数方程组的复杂性，按交替方向隐式差分格式，采用迭代与全选主元高斯约当消去法相结合的方法求解方程：即确定系数矩阵采用迭代法，求解线性方程组时采用全选主元高斯约当消去法，在研究模型解法的同时按FORTRAN结构化程序设计的要求，编制计算机程序，形成相应的CBMRS计算机模型，并通过模型的运行从理论上证明了模型的正确性与可靠性。

The description methods of natural scenery was studied based on fractal, that is, recursive method, L-system method, IFS and IFS description method was put forward based on sine or cosine. This method overcomes angularity and consistency of recursive method, L-system method and IFS, and the variety of fractal sculpting consequence can be added and the basis for the later research and the application was provided.

对基于分形的描述自然景物方法，即递归洪、L-系统法、IFS法进行了分析研究，在此基础上，提出基于正余弦的IFS描述法，该方法克服了递归法、L-系统法、IFS法等描述方法的生硬性和一律性，增加了分形造型结果的多样性，为以后的深入研究和应用提供了依据。

The CBRC allows commercial banks to implement the internal rating method by stages, however, when a commercial bank obtains the approval for using the internal rating method, its asset coverage ratio calculated according to the internal rating method (risk-weighted assets calculated according to the internal rating method)/(risk-weighted assets calculated according to the internal rating method + risk-weighted assets of other credit risk exposures calculated according to the revised capital supervisory provisions) shall not be lower than 50%, and it shall formulate the plan for the implementation of internal rating method by stages, so as to ensure that the asset coverage ratio reach 80% in three years.

银监会允许商业银行分阶段实施内部评级法，但在获得许可使用内部评级法时，采用内部评级法的资产覆盖率（按内部评级法计算的风险加权资产/［按内部评级法计算的风险加权资产＋按修订后资本监管规定计算的其他信用风险暴露的风险加权资产］）应不低于50％，并制定分阶段实施内部评级法规划，以保证3年内资产覆盖率达到80％。

In chapter 2,all kinds of numerical methods of computational fracturemechanics are summarized,the development histories and present situation ofboundary collocation method,boundary integral method,finite difference method,boundary element method and finite element method are expounded,and theapplication of finite element method in fracture mechanics are emphaticallydiscussed.

第二章 总结了计算断裂力学中各种数值方法，论述了边界配位法、边界积分法、有限差分法、边界元法及有限元法的发展历史和现状，并着重讨论了有限元法在断裂力学中的应用。

The stress analytic method of arch dam covers pure arch method, arch beam sharing method, finite element method, calculating method of shell theory and structural model test method.

拱坝的应力分析方法包括纯拱法、拱梁分载法、有限元法、壳体理论计算方法和结构模型试验法。

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

在侵犯著作权案件中，如果被控侵权行为人虽未经著作权人的同意，使用甚至抄袭了受著作权保护的作品或作品的片段，但若情节轻微，未对该作品的正常使用产生任何实质不利的影响，亦未对权利人的权利造成实质性的损害，则应适用&不计琐细原则&，免除行为人的责任，以寻求在权利人利益与著作权法所体现的社会公共利益之间的平衡。

This new product will become our best seller.

这个新产品会成为我们最畅销的产品。