一维插值实验报告.docx

一维插值实验报告.docx一维插值实验报告
一、实验内容
对函数曲）=歯
(1)
把区间分成等份，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)
(4)
分段插值作图,n=5,10, 20, 50,100
三次样条插值作图，n=5,10, 20, 50,100
二、实验设计
编程如下:
untitled
clc
x=linspace (-1,1,11);
y=l./(l+25*); xO=linspace (-1z1r5);
yO=l./(l+25*);
yl=interpl(x,y,xO, 1 spline 1) y2=interpl(xz y,xO);
A=[ones (llf 1) xf (x. A2) 1 (x. A3) 1 (x. A4) 1 (x. A5) 1 (x. A6) 1 (x. A7) 1 (x. A8) 1 () 1 () * ]
a=A\y1;
y3=
a(1)+a(2) .*x0+a(3) .*+a(4) .*+a(5) .*+a(6) .*+a(7) .*x
+a(8) .*+a (9) .* + a (10) .*+a (11) .*;
plot (xO,y3, 1r1),
gtext ('),
hold onf
plot(xO,y2,f), gtext('.')/
hold on,
plot(xO,yl, 1 m1 ),
gtext(1 Spline 1)
hold off

clc
x=linspace (-1,1,11);
y=l./(l+25*);
xO=linspace(-1,1,10);
y0=l./(l+25*);
yl = interpl(x,yf xO, 1 spline 1)
y2=interpl(x,y,xO);
A=[ones (11, 1) x * () * () * () ' () ' ( 6) * () * () *
() 1 () 1 ]
a=A\y1;
y3=
a(1)+a(2) .*x0+a(3) .*+a (4) .*+a (5) .*+a (6) .*+a (7) .*x
+a (8) .*+a(9) .*+a(10) .*+a (11) .*;
plot (x0,y3, 1r*),
gtext(),
hold on,
plot(xO,y2,'b'),
gtext('.'),
hold on,
plot(xO,yl,1m1),
gtext (1 Spline 1)
hold off

clc
x=linspace(-1,1,11);
y=l./(l+25*);
xO=linspace(-1f1< 20);
y0=l./(l + 25*x. A2);
yl=interpl(x,y,x0z 1 spline 1)
y2=interpl(xz yz xO);
A=[ones (11, 1) x1 (x. A2) 1 (x."3) * (x. A4) ' (x. A5) ' (x. A6) 1 (x. A7) * (x. A8) *
()1 ()1]
a=A\y1;
y3=
a (1)+a (2) .*xO+a (3) .*+a(4) .*+a(5) .*+a(6) .*+a (7) .*x
+a(8) .*+a (9) .*+a (10) .*+a (11) .*;
plot(x0z y3z 1r1)z
gtext( ) r
hold on,
plot(x0z y2, 'b1),
gtext('.'),
hold on,
plot(xO,yl,1m1),
gtext (1 Spline 1)
hold off

clc
x=linspace (-1,1,11);
y=l./(l+25*);
xO=linspace(-1,1,50