Update 2024-06-21-GAMES001-NOTES-12.md

peng00bo00 · Jun 21, 2024 · ea7cabe · ea7cabe
1 parent e13dec9
commit ea7cabe
Showing 1 changed file with 19 additions and 0 deletions.
diff --git a/_posts/2024-06-21-GAMES001-NOTES-12.md b/_posts/2024-06-21-GAMES001-NOTES-12.md
@@ -221,6 +221,25 @@ $$
 
 ### 子空间迭代
 
+除了前面介绍的不动点迭代方法，另一种常用的迭代求解线性系统的方法为子空间迭代法。
+
+<div align=center>
+<img src="https://search.pstatic.net/common?src=https://i.imgur.com/MlERVme.png" width="100%">
+</div>
+
+子空间迭代法中最常用的方法是[Krylov子空间迭代法](https://en.wikipedia.org/wiki/Krylov_subspace)。
+
+<div align=center>
+<img src="https://search.pstatic.net/common?src=https://i.imgur.com/XbJEgEj.png" width="100%">
+</div>
+
+在Krylov子空间的基础上，对于对称半正定系数矩阵的情况我们可以推导[共轭梯度下降法](https://en.wikipedia.org/wiki/Conjugate_gradient_method)。
+
+<div align=center>
+<img src="https://search.pstatic.net/common?src=https://i.imgur.com/XT58RZk.png" width="100%">
+<img src="https://search.pstatic.net/common?src=https://i.imgur.com/nWNDdII.png" width="100%">
+</div>
+
 ## Reference
 
 - [Lecture 13: 线性系统](https://www.bilibili.com/video/BV1MF4m1V7e3?p=13&vd_source=7a2542c6c909b3ee1fab551277360826)