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科学计算引论
电子课件：
课程介绍，
线性代数基础，
数值计算中的误差
参考资料：
矩阵论 (戴华, 科学出版社, 2001)
Matrix Analysis, 2nd Edition (Horn & Johnson, 2013)
Linear Algebra and Its Applications, 5th Edition (Lay et al., 2016)
Introduction to Linear Algebra, 5th Edition (Strang, 2016)
课外阅读：
科学计算：科技创新的第三种方法 (陈志明, 2012, 数学)
浅谈科学计算 (朱少平, 2009, 物理)
The Best of the 20th Century: Editors Name Top 10 Algorithms (SIAM News & CiSE, 2000)
课后作业：1.1, 1.2, 1.4, 1.6, 1.8
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非线性方程数值解法
电子课件：
对分法/不动点迭代法/Steffensen 迭代法，
Newton 迭代法/割线法/抛物线法
参考资料：
非线性方程组数值方法 (范金燕, 袁亚湘, 2018)
Iterative Methods for Linear and Nonlinear Equations (Kelley, 1995)
Solving Nonlinear Equations with Newton's Method (Kelley, 2003)
MATLAB 示例代码：
code02.rar
课后作业：2.1, 2.2, 2.3, 2.5; 可选题: 2.4, 2.6, 2.7, 2.8
上机练习：hwm202501.pdf
(MATLAB 模板供参考: hw11t.m)
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线性方程组直接解法
电子课件：
Gauss 消去法/矩阵分解法，
扰动分析/解的改进
参考资料：
Matrix factorizations and direct solution of linear systems (Beattie, Handbook of LA, 2014)
Gaussian Elimination (Higham, 2011)
The decompositional approach to matrix computation (Stewart, 2000)
Map of Matrix Decomposition I (Lu, 2022)
Map of Matrix Decomposition II (Lu, 2022)
课外阅读：
Mathematicians of Gaussian Elimination (Grcar, Notices of the AMS, 2011)
A survey of direct methods for sparse linear systems (Davis et al., 2016)
Direct Methods for Sparse Matrices, 2nd Edition (Duff et al., 2017)
Direct Methods for Sparse Linear Systems (Davis, 2006)
Numerical algorithms for high-performance computational science (Dongarra, Grigori & Higham, 2020)
MATLAB 示例代码：
code03.rar
课后作业：3.1, 3.3, 3.4, 3.5, 3.7, 3.8, 3.10; 可选题: 3.2, 3.6, 3.9, 3.11, 3.12
上机练习：
hwm202502.pdf
(数据文件: data_hw22.mat,
MATLAB 模板供参考: hw21t.m, hw22t.m)
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线性方程组迭代解法
电子课件：
定常迭代法，
收敛性分析/经典迭代法的收敛性，
最速下降法与共轭梯度法
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
MATLAB 示例代码：
code04.rar
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线性最小二乘问题
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函数插值
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数值积分与数值微分