数学实验十五.doc

玉溪师范学院数学系
《数学实验》报告

班级 10级数学一班 学号 2010011132 姓名 王正胡 成绩
实验内容：
1.简单迭代与不动点。
2.牛顿迭代法、割线法。
一、实验目的
1．了解迭代法的基本思想。
2．体验非线性方程迭代法的发展历程。
二、预备知识
1．了解迭代的基本概念。
2．不动点的基本概念和相关定理。
3．牛顿迭代法原理。
4．迭代MATLAB有关命令。
三、实验内容与要求（本部分内容为主要内容）
Matlab命令
结果
15.1
clear
p(1)=1.4;
for i=1:20
p(i+1)=1+p(i)-p(i)^2/4;
end
p

（2）

p(1)=-2.05;
for i=1:20
p(i+1)=1+p(i)-p(i)^2/4;
end
p
15.1

for i=1:10
x1(2*i+1)=y(i);
x1(2*i)=x1(2*i-1);
y1(2*i)=y(i);
y1(2*i+1)=y1(2*i);
end
x2=1:0.01:3;
y2=x2;
y1+x2-x2.^2/4;
plot(x1,y1,'k0-'x2,y2,'r',x2,y3,'b')
axis([1.3,2.1,1.85,2.1])
legeng('迭代线','迭代函数','y=x')
15.2
clear;
d(1)=19;
for i=1:20
d(i+1)=(9585/(45-d(i)))^91/2);
end

15.3
clear
x(1)=19;
for i=1:10
x(i+1)=x(i)-(x(i)^3-45*x(i)^2+9585)/(3*x(i)^2-90*x(i))
end
15.4
>> clear;
x=0.0;
for i=1:6
x=x-(x*exp(x)-1)/((x+1)*exp(x))
end
15.4（2）
clear;
x=10.0;
for i=1:20
x=x-(x*exp(x)-1)/((x+1)*exp(x))
end
15.1
p =

Columns 1 through 3

1.4000 1.9100 1.9980

Columns 4 through 6

2.0000 2.0000 2.0000

Columns 7 through 9

2.0000 2.0000 20000

Columns 10 through 12

2.0000 2.0000 2.0000

Columns 13 through 15

2.0000 2.0000 2.0000

Columns 16 through 18

2.0000 2.0000 2.0000

Columns 19 through 21

2.0000 2.0000 2.0000
（2）
p =

1.0e+177 *

Columns 1 through 3

-0.0000 -0.0000 -0.0000

Columns 4 through 6

-0.0000 -0.0000 -0.0000

Columns 7 through 9

-0.0000 -0.0000 -0.0000

Columns 10 through 12

-0.0000 -0.0000 -0.0000

Columns 13 through 15

-0.0000 -0.0000 -0.0000

Columns 16 through 18

-2.4348 -Inf -Inf

Columns 19 through 21

-Inf -Inf -Inf

15.3
x =

19.0000 19.3174

x =

19.0000 19.3174 19.3194

x =

Columns 1 through 3

19.0000 19.3174 19.3194

Column 4

19.3194

x =

Columns 1 through 3

19.0000 19.3174 19.3194

Columns 4 through 5

19.3194 19.3194

x =

Columns 1 through 3

19.0000 19.3174 19.3194

Columns 4 through 6

19.3194 19.3194 19.3194

x =

Columns 1 through 3

19.0000 19.3174 19.3194

Columns 4 through 6

19.3194 19.3194 19.3194

Column 7

19.3194

x =

Columns 1 through 3

19.0000 19.3174 19.3194

Columns 4 through 6

19.3194 19.3194 19.3194

Columns 7 through 8

19.3194 19.3194

x =

Columns 1 through 3

19.0000 19.3174 19.3194

Columns 4 through 6

19.3194 19.3194 19.3194

Columns 7 through 9

19.3194 19.3194 19.3194

x =

Columns 1 through 3

19.0000 19.3174 19.3194

Columns 4 through 6

19.3194 19.3194 19.3194

Columns 7 through 9

19.3194 19.3194 19.3194

Column 10

19.3194

x =

Columns 1 through 3

19.0000 19.3174 19.3194

Columns 4 through 6

19.3194 19.3194 19.3194

Columns 7 through 9

19.3194 19.3194 19.3194

Columns 10 through 11

19.3194 19.3194

>>
15.4
x =

1

x =

0.6839

x =

0.5775

x =

0.5672

x =

0.5671

x =

0.5671

>>
15.4（2）
x =

9.0909

x =

8.1900

x =

7.2989

x =

6.4194

x =

5.5544

x =

4.7076

x =

3.8844

x =

3.0933

x =

2.3487

x =

1.6759

x =

1.1195

x =

0.7453

x =

0.5902

x =

0.5676

x =

0.5671

x =

0.5671

x =

0.5671

x =

0.5671

x =

0.5671

x =

0.5671

>>
三、实验后记
（记录实验的一些重要之处及其所涉及的一些更深层次的实验现象，包括所查询的参考资料也应该将其记录下来！）
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