共轭梯度法

This multigrid solver is proven to provide the same accuracy as the finite element solution with respect to energy norm, and the computational complexity is suboptimal.

并证明用共轭梯度法作迭代算子时，该方法可以达到能量模意义下的最优，计算复杂度接近最优。

And the equations are solved coupling iteratively whith PCG method for Laplace equation and Gauss—Seidel method for convective equation.So the distribution of piezometric tube waterhead and saturation can be obtained.And the seepace free surface will be captured automatically according to the distribution of saturation with the concept of VOF.

分别对饱和区的拉普拉斯方程采用预处理共轭梯度法、非饱和区的对流方程采用Gauss—Seidel方法进行耦合迭代求解，得到渗流场的测压管水头分布和饱和度分布，并引入VOF的概念，由饱和度的分布自动扑捉渗流自由面。

One points at a sequence of one sparse linear algebra system of equation ,utilizing frequent treatment sparse matrix data structure at present that is according to the competent store structure, design the law of conjugation gradient method which solves the equation group of the sparse linear algebra of asking analyses the complexity of calculating.

第一部分针对一类稀疏线性代数方程组，利用目前国际上使用比较频繁的处理稀疏矩阵的按行稀疏存储结构，设计了求解稀疏线性代数方程组的共轭梯度法，并分析计算复杂度。

The one order differential model and convolutional model of impedance formula of amplitude versus offset inversion were established. Impedance inversion formula from AVO was derived based on Bayesian framework. Methods of using Huber function as prior model parameter distribution and covariance matrix from well log as constrains were developed. The P-wave impedance, S-wave impedance and density were calculated by the conjugate gradient algorithm.

为此建立了振幅随偏移距变化波阻抗反演公式的一阶差分模型及褶积模型，推导了基于贝叶斯理论的AVO波阻抗反演公式，给出了采用Huber分布作为模型参数的先验分布及测井数据的参数协方差矩阵作为约束条件的实现方法，并利用共轭梯度法计算了纵、横波阻抗及密度。

Preconditioned con- jugate gradient algorithm is a fast and accurate computational algorithm.

预条件共轭梯度法是一种精确并且收敛迅速的计算方法。

The PetrovGalerkin formulation is applied to solve the genera lized Stokes problem in each subdomain, and the Lagrange multiplier problem on the interfaces is solved using an algorithm of conjugated gradient. Velocity, density and Lagrange multiplier are approached in the spaces of continue piecewise linear functions.

应用PetrovGalerkin方法解每个子域上的广义Stokes问题，而交界面上的Lagrange乘子则通过共轭梯度法迭代求解，各变量均由线性函数离散。

On the base of the good convergence of FR, and in view of the descend property of the paper presents a new conjugate gradient method, and studies the global convergence with two kinds of Armijo-type linear search.

基于FR方法好的收敛性并考虑到d的下降性，提出了一类新的共轭梯度法，并在两种Armijo型搜索下，研究了新方法的全局收敛性。

Numerical examples show that the least- squares images can be efficiently retrieved in a few iterations of conjugate gradients method.

数值实例表明，通过少数的共轭梯度法迭代，就能得到与真实模型差别很微小的偏移效果。

In inner loop,we use a modified conjugate gradient algorithm and a restarted technique; in outer loop, the Morozov's discrepancy principle is used as a stopping rule.

该方法的内层循环采用修改的共轭梯度法，并使用重开始技巧；外层循环使用Morozov偏差准则作为停机准则。

Conjugate gradient methods are very important for solving nonlinear optimization problems.

共轭梯度法是解决无约束非线性最优化问题的重要的方法之一。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。