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2016011528_张嘉玮_大作业二_报告1
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2.1 程序截图8 2.2【求 】 2.2.1 泰勒展开求 2.2.1.1 算法原理10 2.2.1.2 误差分析10 2.2.1.3 程序框图11 2.2.1
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《数值分析与算法》_第二次大作业_自 61_张嘉玮_2016011528
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第 1 页 共 51 页
《数值分析与算法》
数值方法求
X
张嘉玮
自 61
2016011528
2018 年 12 月 22 日星期六
![](https://csdnimg.cn/release/download_crawler_static/86333359/bg2.jpg)
《数值分析与算法》_第二次大作业_自 61_张嘉玮_2016011528
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第 2 页 共 51 页
目录
1、 需求分析
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8
2. 算法设计与分析
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8
2.1 程序截图
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8
A、 泰勒展开
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8
B、 改进的泰勒展开
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8
C、 数值积分之复化梯形公式
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8
A、 改进的泰勒展开
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8
B、 数值积分之梯形梯形公式
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8
C、 数值积分之复化辛普生公式
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8
A、 泰勒展开
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8
B、 改进的欧拉方法
..............................................................................................................
8
C、 方程求根结合辛普生公式
..............................................................................................
8
2.2【求
】
2.2.1 泰勒展开求
2.2.1.1 算法原理
.............................................................................................................................
10
2.2.1.2 误差分析
.............................................................................................................................
10
A、 方法误差
........................................................................................................................
10
B、 舍入误差
........................................................................................................................
11
C、 综合考虑各种误差,总误差为:
................................................................................
11
2.2.1.3 程序框图
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11
2.2.1.4 计算代价
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13
2.2.1.5 收敛速度
.............................................................................................................................
13
2.2.1.6 实验
.....................................................................................................................................
13
2.2.2 改进的泰勒展开求
2.2.2.1 算法原理
.............................................................................................................................
13
2.2.2.2 误差分析
.............................................................................................................................
14
A、 方法误差
........................................................................................................................
14
B、 舍入误差
........................................................................................................................
14
C、 将两类误差求和便得到了总的误差:
........................................................................
15
2.2.2.3 程序框图
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15
2.2.2.4 计算代价
.............................................................................................................................
17
2.2.2.5 收敛速度
.............................................................................................................................
17
2.2.2.6 实验
.....................................................................................................................................
17
2.2.3 数值积分之复化梯形公式求
2.2.3.1 算法原理
.............................................................................................................................
17
2.2.3.2 误差分析
.............................................................................................................................
18
A、 方法误差
........................................................................................................................
18
![](https://csdnimg.cn/release/download_crawler_static/86333359/bg3.jpg)
《数值分析与算法》_第二次大作业_自 61_张嘉玮_2016011528
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第 3 页 共 51 页
B、 舍入误差
........................................................................................................................
19
C、 将两类误差求和便得到了总的误差:
........................................................................
19
2.2.3.3 程序框图
.............................................................................................................................
19
2.2.3.4 计算代价
.............................................................................................................................
21
2.2.3.5 收敛速度
.............................................................................................................................
21
2.2.3.6 实验
.....................................................................................................................................
21
2.2.4 方法比较
................................................................................................................................
21
2.3 【
ln
】
2.3.1 改进的泰勒展开
ln
2.3.1.1 算法原理
.....................................................................................................................
22
2.3.1.2 误差分析
.....................................................................................................................
22
A、 方法误差
........................................................................................................................
22
B、 舍入误差
........................................................................................................................
23
C、 PI 引起的误差
................................................................................................................
23
D、 总的误差
........................................................................................................................
24
2.3.1.3 程序框图
.....................................................................................................................
24
2.3.1.4 计算代价
.....................................................................................................................
26
2.3.1.5 收敛速度
.....................................................................................................................
26
2.3.1.6 实验
.............................................................................................................................
26
2.3.2 数值积分之梯形梯形公式
ln
2.3.2.1 算法原理
.....................................................................................................................
26
2.3.2.2 误差分析
.....................................................................................................................
27
A、 方法误差
........................................................................................................................
27
B、 舍入误差
........................................................................................................................
28
C、 PI 引起的的误差
............................................................................................................
28
D、 总的误差
........................................................................................................................
28
2.3.2.3 程序框图
.....................................................................................................................
29
2.3.2.4 计算代价
.....................................................................................................................
31
2.3.2.5 收敛速度
.....................................................................................................................
31
2.3.2.6 实验
.............................................................................................................................
31
2.3.3 数值积分之复化辛普生公式
ln
2.3.3.1 算法原理
.....................................................................................................................
31
2.3.3.2 误差分析
.....................................................................................................................
32
A、 方法误差
........................................................................................................................
32
B、 舍入误差
........................................................................................................................
32
C、 PI 引起的的误差
............................................................................................................
33
E、 总的误差
........................................................................................................................
33
2.3.3.3 程序框图
.....................................................................................................................
34
2.3.3.4 计算代价
.....................................................................................................................
36
2.3.3.5 收敛速度
.....................................................................................................................
36
![](https://csdnimg.cn/release/download_crawler_static/86333359/bg4.jpg)
《数值分析与算法》_第二次大作业_自 61_张嘉玮_2016011528
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第 4 页 共 51 页
2.3.3.6 实验
.............................................................................................................................
36
2.3.4 方法对比
................................................................................................................................
36
2.4 【
X
】
2.4.1 泰勒展开
X
2.4.1.1 算法原理
.....................................................................................................................
37
2.4.1.2 误差分析
.....................................................................................................................
37
A. 方法误差
...........................................................................................................................
37
B. 舍入误差
...........................................................................................................................
38
D. 总误差
...............................................................................................................................
39
2.4.1.3 程序框图
.....................................................................................................................
39
2.4.1.4 计算代价
.....................................................................................................................
41
2.4.1.5 收敛速度
.....................................................................................................................
41
2.4.1.6 实验
.............................................................................................................................
41
2.4.2 改进的欧拉方法
X
2.4.2.1 算法原理
.....................................................................................................................
41
2.4.2.2 误差分析
.....................................................................................................................
41
A. 方法误差
...........................................................................................................................
41
B. 舍入误差
...........................................................................................................................
42
D、总误差
..............................................................................................................................
43
2.4.2.3 程序框图
.....................................................................................................................
43
2.4.2.4 计算代价
.....................................................................................................................
45
2.4.2.5 收敛速度
.....................................................................................................................
45
2.4.2.6 实验
.............................................................................................................................
45
2.4.3 程求根结合辛普生公式
X
2.4.3 方程求根与数值积分
....................................................................................................
45
2.4.3.1 算法原理
.....................................................................................................................
45
2.4.3.2 误差分析
.....................................................................................................................
46
A、 牛顿法误差
....................................................................................................................
46
B、 Ln(PI)的误差所导致的误差
..........................................................................................
47
C、 复化辛普生公式的误差
................................................................................................
47
D、 舍入误差
........................................................................................................................
48
E、 总误差
............................................................................................................................
49
2.4.3.3 程序框图
.....................................................................................................................
49
2.4.3.4 计算代价
.....................................................................................................................
51
2.4.3.5 收敛速度
.....................................................................................................................
51
2.4.3.6 实验
.............................................................................................................................
51
2.4.4 方法对比
................................................................................................................................
51
3. 收获反思
.............................................................................................................................................
52
4、 参考文献
..........................................................................................................................................
53
[1] 李庆扬、王能超、易大义. 数值分析(第五版)
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53
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