Conjugate Gradient Method 共轭梯度法(Conjugate Gradient Method) 是一种用于求解线性方程组 Ax=b 的迭代算法,其中 A 是一个对称正定矩阵。这种方法特别适用于大规模稀疏矩阵问题,常见于数值分析和科学计算领域。共轭梯度法由Magnus Hestenes和Eduard Stiefel于1952年提出。 基本思想 共轭
Conjugate Gradient Method Example: Solve: 10 -1 2 0 -1 11 -1 3 2 -1 10 -1 0 3 -1 8 k=1 k=2 k=3 k=4 x1 x2 x3 X4 0 0.4716 0.9964 1.0015 1.0000 0 1.9651 1.9766 1.9833 2.0000 0 -0.8646 -0.9098 -1.0099 -1.0000 0 1.1791 1.0976 1.0197 1.0000 31.7 5.1503 1.0433 0.1929 0.0000...
By combining Newton iterations with conjugate gradient iterations, the NCG method achieves a comparable number of iterations to Newton's method but is significantly faster overall and better suited at finding complex solutions. Using bulk solitons in a nonlinear photonic Chern insulator as an example,...
。 5 共轭梯度法 共轭梯度法,Conjugate gradient method,是一种求解对称正定线性方程组Ax=b的迭代方法。 共轭梯度法是介于梯度下降法与牛顿法之间的一个方法,是一个一阶方法。它克服了梯度下降法收敛慢的缺点,又避免了存储和计算牛顿法所需要的二阶导数信息。 适用 二次规划问题。 思想 共轭梯度法的基本思想是把...
The Conjugate Gradient Method is a technique that involves generating mutually conjugate direction vectors based on the gradient vector for functional optimization in the control domain. It computes a new control function in each iteration by utilizing the gradient. ...
Begtostudy(白途思)'s Professional Technology Blog 共轭梯度法/Conjugate Gradient Method 共轭梯度法是介于最速下降法与牛顿法之间的一个方法,它 仅需利用一阶导数信息,但克服了最速下降法收敛慢的缺点,又避免了牛顿法需要存储和计算Hesse矩阵并求逆的缺点,共轭梯度法不仅是解决大型线性方程组最有用的方法之一,...
Begtostudy(白途思)'s Professional Technology Blog 共轭梯度法/Conjugate Gradient Method 共轭梯度法是介于最速下降法与牛顿法之间的一个方法,它 仅需利用一阶导数信息,但克服了最速下降法收敛慢的缺点,又避免了牛顿法需要存储和计算Hesse矩阵并求逆的缺点,共轭梯度法不仅是解决大型线性方程组最有用的方法之一,...
【Numberical Optimization】5 Conjugate Gradient Methods (zen学习笔记),程序员大本营,技术文章内容聚合第一站。
1. Wave equation and the finite difference method 1. Imaging 3. Boundary saving scheme Design information of L1 primitives 1. Stencil2D 1. RTM2D Forward streaming module Backward streaming module 3. Stencil3D 1. RTM3D Conjugate Gradient Solver Introduction Conjugate Gradient Algorith...
The conjugate gradient method is an ingenious method for iterative solution of sparse linear equations. It is now a standard benchmark for parallel scientific computing. In the author's opinion, the apparent mystery of this method is largely due to the inadequate way in which it is presented ...