共轭梯度法

Taking range as the performance function, considering end velocity, height and trajectory slope angle constraints, the optimal glide trajectory was solved by maximum principle of Pontryagin and conjugate-gradient method.

建立了滑翔弹道模型，以射程为指标函数，考虑终端速度、高度和弹道倾角约束，采用庞特里亚金极大值原理和共轭梯度法求出控制变量有约束的最优滑翔弹道，简要分析了滑翔增程机理。

Assuming the independence (or the weak-correlation) between the reflectivity and wavelet, the optimal estimation equations for the wavelet and reflectivity were derived respectively. Furthermore, pre-conditional conjugate gradient algorithm iteration inversion was applied to realize the simultaneous estimation of reflectivity and wavelet.

基于反射系数与子波相互独立的假设，分别构建了反射系数和子波最优估计方程，并采用预条件共轭梯度法迭代反演实现反射系数和子波的同时估计。

The global convergence properties of the conjugate gradient methods for the unconstrained optimization problems are studied in this dissertation.

本文集中对求解无约束最优化问题的有效方法—共轭梯度法的全局收敛性进行分析。

This paper presents some new conjugate gradient methods for unconstrained optimization.

本文主要考虑求解无约束最优化问题的共轭梯度法。

The geology research of carbonate reservoirs in Ordovician of Tahe oilfield showed that many large dissolved vugs and fractures were developed. The spread of the reservoir take on a very heterogeneous state. And the typical fractured-vuggy reservoirs was formed. According to the combination of the various spaces, the formation was divided into vuggy formation, fractured-vuggy formation and fractured formation. The research showed that development of the vug is relevant to the its position on the structure, the fractures, the water surface and the weathering surface. Multi-phase charge and recharge of the oil in the reservoirs resulted in the complexity of the fluid distribution. So the"Bottle Model"was brought forward to explain the movement of the water-oil contact. The special storage space and the complex fluid distribution lead to the unstability of the production and the complexity of the water cut. In order to explain the characteristic of the fracture-vug unit was brought forward and the basic principle and method of the partition of the fracture-vug unit was formed. The classification and evaluation of the units were performed according the reserve and energy. Based on the research of geology characteristic and the fluid flow in the reservoir the comprehensive numerical simulation plan of the fractured-vuggy reservoirs were established. Through the selection of the simulation unit, fluid flow type and parameter equivalent the triple media reservoir simulation model was established. Considering the practical application the model was resolved by the DKR decomposition conjugate grads method. Based on the fine reservoir description of Dsitrict IV of the Tahe oilfield the various space type were classified and combined together. The geology model of Unit S48 was constructed. Two typical single well model was established according to the geology and the dynamic phenomena. Finally the single well model and the Unit S48 were simulated by the triple media reservoir simulator. Via the local grid refinement and coarsening in the simulation good matchs were gained. Based on the results of the simulation the reserve distribution, percent of reserve produced in various space and the natural energy were analyzed. The fluid was storaged in the fractures and vugs mostly and more than 90% the produced oil came from the systems. The energy belonged to the active one. The results of simulation accorded with the fact and showed the validity and practicability the research and the simulator.

塔河油田奥陶系碳酸盐岩油藏的地质研究表明，其储层中发育着很多大型的溶蚀洞、缝，储层的平面展布呈现出极度的非均质性，形成了典型的缝洞型碳酸盐岩油藏，根据各种孔隙介质在储层中的组合，将储层分为了溶洞型、裂缝-溶洞型和裂缝型三类；研究表明溶洞储层的发育和构造位置、裂缝的发育、潜水面和风化面的位置等因素有关；多期充注的油气成藏模式导致了流体复杂的赋存状态，由此提出了所谓的"瓶子模型"，解释生产过程中油水界面的变化；特殊的储集空间类型和流体分布特征导致油田在开发过程中表现出很大的不确定性和含水变化的复杂性，为了合理的解释油气田开发过程中的动态特征，提出了"缝洞单元"的概念，并制定了"缝洞单元"纵横向划分的基本原则和依据及划分方法，并对"缝洞单元"进行了分类和评价；基于地质特征和流体在其中流动规律的研究，提出了缝洞型碳酸盐岩油藏的数值模拟综合解决方案，通过模拟单元的选择、流动类型和参数的等效，建立了三重介质油藏三维三相数值模拟模型，采用不完全LU分解预处理共轭梯度法进行了求解；在塔河油田4区精细油藏描述的基础上，将各种类型的孔隙空间进行了归类组合，建立了S48单元的地质模型；通过对油井生产动态进行分析研究，建立了两类和油井地质、生产动态相对应的单井模型；最后应用三重介质油藏数值模拟软件对单井模型和S48单元进行了数值模拟，通过局部加密和粗化等技术模拟流体流动规律，取得了很好的拟合效果；结合数值模拟结果，分析了各种介质中的储量分布、储量产出的百分比以及地层的能量，认为塔河油田缝洞型油藏中流体绝大多数储集于缝洞系统之中，所产出流体90%以上也来自于缝洞系统，其底水能量属于较充足的类型；模拟结果和油田实际情况符合较好，说明了地质研究和油藏数值模拟研究的正确性。

The solutions of ProblemⅠ,ⅡandⅢare discussed by using the generalized conjugate gradient method. When the equation is consistent, the solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are successfully found; When the equation is inconsistent, the least-squares solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are also found successfully. The generalized conjugate gradient method has the following traits:(1) It can judge automatically the information of solutions.

利用广义共轭梯度法，讨论了问题Ⅰ、Ⅱ和Ⅲ解的情况：当方程相容时，研究了方程的一般解、对称解、中心对称解、自反矩阵解、双对称解、对称次反对称解及其最佳逼近等问题；当方程不相容时，研究了方程的最小二乘一般解、最小二乘对称解、最小二乘中心对称解、最小二乘自反矩阵解、最小二乘双对称解、最小二乘对称次反对称解及其最佳逼近等问题。

By using active set strategy, the authors need only to solve a reduced trust region subproblem which is solved inexactly by the truncated conjugate gradient method.

作者利用有效集策略，在每次迭代中只需求解一个低维的信赖域子问题，该信赖域子问题是通过截断共轭梯度法来近似求解的。

Using Huber function, the method can alleviate the oversmooth problem at the "motion edge". To get the displacement field, the conjugated gradient method is used to minimize the energy function.

该算法采用共轭梯度法优化能量方程，并利用小波分解进行分级计算，能快速可靠地得到稳定的位移场。

Second was the emergence of preconditioned conjugate gradient-like methods for solving linear systems.

第二个是预处理似共轭梯度法的出现。

The geology research of carbonate reservoirs in Ordovician of Tahe oilfield showed that many large dissolved vugs and fractures were developed. The spread of the reservoir take on a very heterogeneous state. And the typical fractured-vuggy reservoirs was formed. According to the combination of the various spaces, the formation was divided into vuggy formation, fractured-vuggy formation and fractured formation. The research showed that development of the vug is relevant to the its position on the structure, the fractures, the water surface and the weathering surface. Multi-phase charge and recharge of the oil in the reservoirs resulted in the complexity of the fluid distribution. So the"Bottle Model"was brought forward to explain the movement of the water-oil contact. The special storage space and the complex fluid distribution lead to the unstability of the production and the complexity of the water cut. In order to explain the characteristic of the fracture-vug unit was brought forward and the basic principle and method of the partition of the fracture-vug unit was formed. The classification and evaluation of the units were performed according the reserve and energy. Based on the research of geology characteristic and the fluid flow in the reservoir the comprehensive numerical simulation plan of the fractured-vuggy reservoirs were established. Through the selection of the simulation unit, fluid flow type and parameter equivalent the triple media reservoir simulation model was established. Considering the practical application the model was resolved by the DKR decomposition conjugate grads method. Based on the fine reservoir description of Dsitrict IV of the Tahe oilfield the various space type were classified and combined together. The geology model of Unit S48 was constructed. Two typical single well model was established according to the geology and the dynamic phenomena. Finally the single well model and the Unit S48 were simulated by the triple media reservoir simulator. Via the local grid refinement and coarsening in the simulation good matchs were gained. Based on the results of the simulation the reserve distribution, percent of reserve produced in various space and the natural energy were analyzed. The fluid was storaged in the fractures and vugs mostly and more than 90% the produced oil came from the systems. The energy belonged to the active one. The results of simulation accorded with the fact and showed the validity and practicability the research and the simulator.

塔河油田奥陶系碳酸盐岩油藏的地质研究表明，其储层中发育着很多大型的溶蚀洞、缝，储层的平面展布呈现出极度的非均质性，形成了典型的缝洞型碳酸盐岩油藏，根据各种孔隙介质在储层中的组合，将储层分为了溶洞型、裂缝-溶洞型和裂缝型三类；研究表明溶洞储层的发育和构造位置、裂缝的发育、潜水面和风化面的位置等因素有关；多期充注的油气成藏模式导致了流体复杂的赋存状态，由此提出了所谓的&瓶子模型&，解释生产过程中油水界面的变化；特殊的储集空间类型和流体分布特征导致油田在开发过程中表现出很大的不确定性和含水变化的复杂性，为了合理的解释油气田开发过程中的动态特征，提出了&缝洞单元&的概念，并制定了&缝洞单元&纵横向划分的基本原则和依据及划分方法，并对&缝洞单元&进行了分类和评价；基于地质特征和流体在其中流动规律的研究，提出了缝洞型碳酸盐岩油藏的数值模拟综合解决方案，通过模拟单元的选择、流动类型和参数的等效，建立了三重介质油藏三维三相数值模拟模型，采用不完全LU分解预处理共轭梯度法进行了求解；在塔河油田4区精细油藏描述的基础上，将各种类型的孔隙空间进行了归类组合，建立了S48单元的地质模型；通过对油井生产动态进行分析研究，建立了两类和油井地质、生产动态相对应的单井模型；最后应用三重介质油藏数值模拟软件对单井模型和S48单元进行了数值模拟，通过局部加密和粗化等技术模拟流体流动规律，取得了很好的拟合效果；结合数值模拟结果，分析了各种介质中的储量分布、储量产出的百分比以及地层的能量，认为塔河油田缝洞型油藏中流体绝大多数储集于缝洞系统之中，所产出流体90%以上也来自于缝洞系统，其底水能量属于较充足的类型；模拟结果和油田实际情况符合较好，说明了地质研究和油藏数值模拟研究的正确性。

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％。