|
迭代方法与预处理
(Iterative Methods and Preconditioning)
|
|
| |
|
|
|
|
|
| |
课程内容
-
线性方程组定常迭代法
( slides )
经典迭代法, 收敛性分析, 加速方法
参考资料：
Iterative Solution Methods, (O. Axelsson, 1994)
Matrix Iterative Analysis, 2nd Edition (R.S. Varga, 2000)
Iterative Solution of Large Linear Systems, (D.M. Young, 1971)
Matrix Computations, 4th Edition (Golub & van Loan, 2013)
应用举例：Poisson 方程求解
课外阅读：
Iterative methods for linear systems of equations: A brief historical journey,
Saad, 2019
Iterative solution of linear systems in the 20th century,
Saad & van der Vorst, JCAM, 2000
-
线性方程组子空间迭代法
( slides )
Krylov 子空间迭代法, 收敛性分析
参考资料：
Iterative Methods for Sparse Linear Systems, 2nd Edition (Y. Saad, 2003)
Iterative Methods for Solving Linear Systems, (A. Greenbaum, 1997)
Iterative Krylov Methods for Large Linear Systems, (H.A. van der Vorst, 2003)
课外阅读：Five key concepts that shaped iterative solution methods for linear systems, Saad, SIAM News, 2024.
-
线性方程组预处理方法
预处理迭代法, 常用预处理子
参考资料：
Iterative Methods for Sparse Linear Systems, 2nd Edition (Y. Saad, 2003)
Matrix Preconditioning Techniques and Applications (K. Chen, 2005)
课外阅读：
Preconditioning Techniques for Large Linear Systems - A Survey,
Benzi, JCP, 2002
Preconditioning, Wathen, Acta Numerica, 2015
Preconditioners for Krylov subspace methods: An overview,
Pearson & Pestana, GAMM, 2020
A comparison of preconditioned Krylov subspace methods for large-scale nonsymmetric linear systems,
Ghai, Lu & Jiao, NLA, 2018
-
Linux 操作系统介绍
( slides )
Linux 基本使用方法与程序开发环境
参考资料：
Linux Command Quick Reference，
Vi 简介，
Vi 命令小结，
vim cheat sheet
Linux命令行与shell脚本编程大全 (第 4 版), Blum 等著, 2020, 门佳译, 2022
网络资源：
Linux 教程 (http://c.biancheng.net/linux_tutorial)，
Linux 常用命令
Ubuntu 下载：
清华开源软件镜像，
中国科技大学镜像
-
C 语言编程
( slides )
电子讲义：
C 语言程序设计笔记
参考资料：
C Primer Plus (第 6 版), Prata 著, 2014, 姜佑译 2016, 涵盖 C11
零基础学 C 语言 (第 4 版), 康莉等著, 2019
C Reference Card，
常用头文件
网络教程：
C 语言教程 (https://www.runoob.com/cprogramming/c-tutorial.html)
课外阅读：
IEEE浮点运算标准,
矩阵乘积的快速算法
-
并行计算
|
|
| |
- 参考课程：Sparse Matrix Computations, by Y. Saad, 2021.
(https://www-users.cse.umn.edu/~saad/csci8314/)
- 参考课程：
Numerical Methods for Solving Large Scale Eigenvalue Problems, by P. Arbenz, ETH, 2018.
(Lecture Notes)
(http://people.inf.ethz.ch/arbenz/ewp/)
|
|
|
课外阅读：
- V. Simoncini1 and D. B. Szyld,
Recent computational developments in Krylov subspace methods for linear systems,
Numerical Linear Algebra With Applications, 14 (2007), 1--59.
- M. Benzi, G. H. Golub and J. Liesen,
Numerical solution of saddle point problems,
Acta Numerica, (2005), 1--137.
- V. Simoncini and D. B. Szyld
On the Occurrence of Superlinear Convergence of Exact and Inexact Krylov Subspace Methods,
SIAM Review, 47 (2005), 247–-272.
- Jorg Liesen and Petr Tichy,
Convergence analysis of Krylov subspace methods,
GAMM-Mitteilungen, 27 (2004), 153–173.
- A. Hadjidimos,
Successive overrelaxation (SOR) and related methods,
Journal of Computational and Applied Mathematics, 123 (2000) 177--199.
|
|
|
|
|
| |
| |
| |
|
Last modified: September 2023
|