数值分析简明教程.docxVIP

数值分析简明教程

目录

1.内容概括................................................3

1.1数值分析的基本概念...................................4

1.2数值分析与实证分析的区别及其重要性...................5

2.基本理论................................................6

2.1误差与精度...........................................8

2.1.1基本概念与量化误差...............................9

2.1.2截断误差与舍入误差..............................10

2.2收敛性与稳定性......................................11

2.2.1收敛性分析......................................12

2.2.2稳定性分析......................................13

3.计算方法...............................................14

3.1线性插值与拉格朗日插值..............................15

3.2牛顿插值法..........................................15

3.3龙格-库塔法.........................................17

3.3.1基本原理........................................18

3.3.2不同阶数的方法..................................19

4.非线性问题.............................................19

4.1牛顿迭代法..........................................20

4.2詹森法则............................................21

4.3二分法..............................................22

5.矩阵计算...............................................23

5.1矩阵分解............................................24

5.2特殊矩阵运算........................................26

5.2.1正定矩阵与半正定矩阵............................27

5.2.2对称矩阵与三对角矩阵............................29

6.差分方法...............................................30

6.1隐式和显式差分格式..................................30

6.2边界条件处理........................................31

6.3稳定性分析与应用....................................33

7.迭代法.................................................34

7.1雅可比迭代法与共轭梯度法............................35

7.2区间迭代法..........................................36

8.最小二乘法.............................................37

8.1最小二乘原理........................................38

8.2线性最小二乘与非线性最小二乘........................39

9.线性代数基础...........................................40

9.1向量空间与子空间.................