Matlab½øÐÐLagrange¶àÏîʽ²åÖµ
À¸ñÀÊÈÕ²åÖµ·¨¶Ôº¯Êýy=1./(1+25*x.^2)ÔÚÇø¼ä[-1,1]½øÐÐ5´Î¡¢10´Î¡¢15´Î²åÖµ¹Û²ìÁú¸ñÏÖÏó Ö÷³ÌÐò
1£®À¸ñÀÊÈÕ
function [c,l]=lagran(x,y)
%cΪ¶àÏîʽº¯ÊýÊä³öµÄϵÊý %lΪ¾ØÕóµÄϵÊý¶àÏîʽ %xΪºá×ø±êÉϵÄ×ø±êÏòÁ¿ %yΪ×Ý×ø±êÉϵÄ×ø±êÏòÁ¿ w=length(x); n=w-1;
l=zeros(w,w); for k=1:n+1 v=1;
for j=1:n+1 if k~=j
v=conv(v,poly(x(j)))/(x(k)-x(j)) %¶Ô¶àÏîʽ×ö¾í»ýÔËËã end end l(k,:)=v; end c=y*l;
2£®ÔÚmatlab´°¿ÚÖÐÊäÈ룺
x=linspace(-1,1,6);y=1./(1+25*x.^2); lagran(x,y)
»Ø³µ¿ÉµÃ½á¹û£º ans =
-0.0000 1.2019 -0.0000 -1.7308 -0.0000 0.5673 ÔÚmatlab´°¿ÚÖÐÊäÈ룺
x=linspace(-1,1,11);y=1./(1+25*x.^2); lagran(x,y)
»Ø³µ¿ÉµÃ½á¹û£º ans =
-220.9417 0.0000 494.9095 -0.0000 -381.4338 -0.0000 -16.8552 0.0000 1.0000 ÔÚmatlab´°¿ÚÖÐÊäÈ룺
x=linspace(-1,1,16);y=1./(1+25*x.^2); lagran(x,y)
»Ø³µ¿ÉµÃ½á¹û£º ans =
0.0000 123.3597
1.0e+003 *
Columns 1 through 14
0.0000 -1.5189 -0.0000 4.6511 -0.0000 -5.5700 0.0000 3.3477 0.0000 -1.0830 -0.0000 0.1901 -0.0000 -0.0180
Columns 15 through 16
0.0000 0.0010
3.ÓÉÒÔÉϽá¹û¿É¶¨ÒåһϺ¯Êý£º function y=f1(x) y=1./(1+25*x.^2); function y=f2(x)
y=1.2019*x.^4 -1.7308*x.^2+0.5673; function y=f3(x)
y=-220.9417*x.^10+494.9095*x.^8-381.4338*x.^6+123.3597*x.^4-16.8552*x.^2+1; function y=f4(x)
y=1*10^3*(-1.5189*x.^14+4.6511*x.^12-5.5700*x.^10+3.3477*x.^8-1.0830*x.^6+0.1901*x.^4-0.0180*x.^2+0.0010)
4. ÔÚmatlab´°¿ÚÖÐÊäÈ룺
s1=@f1;s2=@f2;s3=@f3;s4=@f4;fplot(s1,[-1 1],'r');hold on;fplot(s2,[-1 1],'k');hold on;fplot(s3,[-1 1],'g');hold on;fplot(s4,[-1 1],'b');xlabel('input');ylabel('output');title('Áú¸ñÏÖÏó');legend('s1=f(x)','s2=L5(x)','s3=L10(x)','s4=L15(X)');grid on ¿ÉÒԵõ½ÏÂͼ£º