一维插值实验报告.docx
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一维插值实验报告.docx
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一维插值实验报告
一维插值实验报告
一、实验内容
对函数
(1)把区间[-1,1]分成等份,并计算f(x)的值
n=5,10,20,50
(2)分别以
(1)中求的值作Lagrange插值,
4次,9次,19次,49次
(3)分段插值作图,n=5,10,20,50,100
(4)三次样条插值作图,n=5,10,20,50,100
二、实验设计
编程如下:
untitled1.m
clc
x=linspace(-1,1,11);
y=1./(1+25*x.^2);
x0=linspace(-1,1,5);
y0=1./(1+25*x.^2);
y1=interp1(x,y,x0,'spline')
y2=interp1(x,y,x0);
A=[ones(11,1)x'(x.^2)'(x.^3)'(x.^4)'(x.^5)'(x.^6)'(x.^7)'(x.^8)'(x.^9)'(x.^10)']
a=A\y';
y3=a
(1)+a
(2).*x0+a(3).*x0.^2+a(4).*x0.^3+a(5).*x0.^4+a(6).*x0.^5+a(7).*x0.^6+a(8).*x0.^7+a(9).*x0.^8+a(10).*x0.^9+a(11).*x0.^10;
plot(x0,y3,'r'),
gtext('lagr.'),
holdon,
plot(x0,y2,'b'),
gtext('Pies.Lin.'),
holdon,
plot(x0,y1,'m'),
gtext('Spline')
holdoff
Untitled2.m
clc
x=linspace(-1,1,11);
y=1./(1+25*x.^2);
x0=linspace(-1,1,10);
y0=1./(1+25*x.^2);
y1=interp1(x,y,x0,'spline')
y2=interp1(x,y,x0);
A=[ones(11,1)x'(x.^2)'(x.^3)'(x.^4)'(x.^5)'(x.^6)'(x.^7)'(x.^8)'(x.^9)'(x.^10)']
a=A\y';
y3=a
(1)+a
(2).*x0+a(3).*x0.^2+a(4).*x0.^3+a(5).*x0.^4+a(6).*x0.^5+a(7).*x0.^6+a(8).*x0.^7+a(9).*x0.^8+a(10).*x0.^9+a(11).*x0.^10;
plot(x0,y3,'r'),
gtext('lagr.'),
holdon,
plot(x0,y2,'b'),
gtext('Pies.Lin.'),
holdon,
plot(x0,y1,'m'),
gtext('Spline')
holdoff
Untitled3.m
clc
x=linspace(-1,1,11);
y=1./(1+25*x.^2);
x0=linspace(-1,1,20);
y0=1./(1+25*x.^2);
y1=interp1(x,y,x0,'spline')
y2=interp1(x,y,x0);
A=[ones(11,1)x'(x.^2)'(x.^3)'(x.^4)'(x.^5)'(x.^6)'(x.^7)'(x.^8)'(x.^9)'(x.^10)']
a=A\y';
y3=a
(1)+a
(2).*x0+a(3).*x0.^2+a(4).*x0.^3+a(5).*x0.^4+a(6).*x0.^5+a(7).*x0.^6+a(8).*x0.^7+a(9).*x0.^8+a(10).*x0.^9+a(11).*x0.^10;
plot(x0,y3,'r'),
gtext('lagr.'),
holdon,
plot(x0,y2,'b'),
gtext('Pies.Lin.'),
holdon,
plot(x0,y1,'m'),
gtext('Spline')
holdoff
Untitled4.m
clc
x=linspace(-1,1,11);
y=1./(1+25*x.^2);
x0=linspace(-1,1,50);
y0=1./(1+25*x.^2);
y1=interp1(x,y,x0,'spline')
y2=interp1(x,y,x0);
A=[ones(11,1)x'(x.^2)'(x.^3)'(x.^4)'(x.^5)'(x.^6)'(x.^7)'(x.^8)'(x.^9)'(x.^10)']
a=A\y';
y3=a
(1)+a
(2).*x0+a(3).*x0.^2+a(4).*x0.^3+a(5).*x0.^4+a(6).*x0.^5+a(7).*x0.^6+a(8).*x0.^7+a(9).*x0.^8+a(10).*x0.^9+a(11).*x0.^10;
plot(x0,y3,'r'),
gtext('lagr.'),
holdon,
plot(x0,y2,'b'),
gtext('Pies.Lin.'),
holdon,
plot(x0,y1,'m'),
gtext('Spline')
holdoff
三、实验结果
y1=
0.03850.14011.00000.14010.0385
A=
Columns1through7
1.0000-1.00001.0000-1.00001.0000-1.00001.0000
1.0000-0.80000.6400-0.51200.4096-0.32770.2621
1.0000-0.60000.3600-0.21600.1296-0.07780.0467
1.0000-0.40000.1600-0.06400.0256-0.01020.0041
1.0000-0.20000.0400-0.00800.0016-0.00030.0001
1.0000000000
1.00000.20000.04000.00800.00160.00030.0001
1.00000.40000.16000.06400.02560.01020.0041
1.00000.60000.36000.21600.12960.07780.0467
1.00000.80000.64000.51200.40960.32770.2621
1.00001.00001.00001.00001.00001.00001.0000
Columns8through11
-1.00001.0000-1.00001.0000
-0.20970.1678-0.13420.1074
-0.02800.0168-0.01010.0060
-0.00160.0007-0.00030.0001
-0.00000.0000-0.00000.0000
0000
0.00000.00000.00000.0000
0.00160.00070.00030.0001
0.02800.01680.01010.0060
0.20970.16780.13420.1074
1.00001.00001.00001.0000
y1=
Columns1through7
0.03850.06170.11570.25720.78590.78590.2572
Columns8through10
0.11570.06170.0385
A=
Columns1through7
1.0000-1.00001.0000-1.00001.0000-1.00001.0000
1.0000-0.80000.6400-0.51200.4096-0.32770.2621
1.0000-0.60000.3600-0.21600.1296-0.07780.0467
1.0000-0.40000.1600-0.06400.0256-0.01020.0041
1.0000-0.20000.0400-0.00800.0016-0.00030.0001
1.0000000000
1.00000.20000.04000.00800.00160.00030.0001
1.00000.40000.16000.06400.02560.01020.0041
1.00000.60000.36000.21600.12960.07780.0467
1.00000.80000.64000.51200.40960.32770.2621
1.00001.00001.00001.00001.00001.00001.0000
Columns8through11
-1.00001.0000-1.00001.0000
-0.20970.1678-0.13420.1074
-0.02800.0168-0.01010.0060
-0.00160.0007-0.00030.0001
-0.00000.0000-0.00000.0000
0000
0.00000.00000.00000.0000
0.00160.00070.00030.0001
0.02800.01680.01010.0060
0.20970.16780.13420.1074
1.00001.00001.00001.0000
y1=
Columns1through7
0.03850.04890.06010.07770.10710.15380.2242
Columns8through14
0.35550.63120.94310.94310.63120.35550.2242
Columns15through20
0.15380.10710.07770.06010.04890.0385
A=
Columns1through7
1.0000-1.00001.0000-1.00001.0000-1.00001.0000
1.0000-0.80000.6400-0.51200.4096-0.32770.2621
1.0000-0.60000.3600-0.21600.1296-0.07780.0467
1.0000-0.40000.1600-0.06400.0256-0.01020.0041
1.0000-0.20000.0400-0.00800.0016-0.00030.0001
1.0000000000
1.00000.20000.04000.00800.00160.00030.0001
1.00000.40000.16000.06400.02560.01020.0041
1.00000.60000.36000.21600.12960.07780.0467
1.00000.80000.64000.51200.40960.32770.2621
1.00001.00001.00001.00001.00001.00001.0000
Columns8through11
-1.00001.0000-1.00001.0000
-0.20970.1678-0.13420.1074
-0.02800.0168-0.01010.0060
-0.00160.0007-0.00030.0001
-0.00000.0000-0.00000.0000
0000
0.00000.00000.00000.0000
0.00160.00070.00030.0001
0.02800.01680.01010.0060
0.20970.16780.13420.1074
1.00001.00001.00001.0000
y1=
Columns1through7
0.03850.04270.04660.05050.05460.05930.0649
Columns8through14
0.07170.08010.09030.10270.11750.13520.1561
Columns15through21
0.18060.20900.24340.28920.35160.43630.5483
Columns22through28
0.68140.81430.92480.99070.99070.92480.8143
Columns29through35
0.68140.54830.43630.35160.28920.24340.2090
Columns36through42
0.18060.15610.13520.11750.10270.09030.0801
Columns43through49
0.07170.06490.05930.05460.05050.04660.0427
Column50
0.0385
A=
Columns1through7
1.0000-1.00001.0000-1.00001.0000-1.00001.0000
1.0000-0.80000.6400-0.51200.4096-0.32770.2621
1.0000-0.60000.3600-0.21600.1296-0.07780.0467
1.0000-0.40000.1600-0.06400.0256-0.01020.0041
1.0000-0.20000.0400-0.00800.0016-0.00030.0001
1.0000000000
1.00000.20000.04000.00800.00160.00030.0001
1.00000.40000.16000.06400.02560.01020.0041
1.00000.60000.36000.21600.12960.07780.0467
1.00000.80000.64000.51200.40960.32770.2621
1.00001.00001.00001.00001.00001.00001.0000
Columns8through11
-1.00001.0000-1.00001.0000
-0.20970.1678-0.13420.1074
-0.02800.0168-0.01010.0060
-0.00160.0007-0.00030.0001
-0.00000.0000-0.00000.0000
0000
0.00000.00000.00000.0000
0.00160.00070.00030.0001
0.02800.01680.01010.0060
0.20970.16780.13420.1074
1.00001.00001.00001.0000
四、实验总结
1.编程时需要注意字母的大小写;
2.调用函数时函数名称需一致;
3.注意题目要求。
五、存在问题
1.编写程序时没有注意字母的大小写,使得程序无法运行;
2.调用函数时,未注意名称是否一致,使得程序无法运行。
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