第04章.zip

% Lagrange插值 clear clc %----------------------------- n=10; %结点个数 lb=-1; %下界 ub=1; %上界 step=0.01; %作图点步长 %----------------------------- % 原始函数图形 x0=lb:step:ub; y0=1./(1+25*x0.^2); plot(x0,y0,'r-'); hold on %----------------------------- % 插值函数 for i=1:n+1 xi(i)=lb+(ub-lb)*(i-1)/n; yi(i)=1/(1+25*xi(i)^2); end %------------------------------ count=1; for x=lb:step:ub fl=0; %-------------------------- %求出pn(xk) for k=1:n+1 up=1; dn=1; %---------------------- %求出f(xk) for i=1:n+1 if k~=i up=up*(x-xi(i)); dn=dn*(xi(k)-xi(i)); end end %---------------------- fl=fl+yi(k)*up/dn; end pn(count)=fl; %-------------------------- fi(count)=1/(1+25*x^2);%求原函数的值 count=count+1; end %------------------------------ % L插值函数图 x=lb:step:ub; plot(x,pn,'g--') %------------------------------ num=(ub-lb)/step+1; for i=1:num p_f(i)=pn(i)-fi(i); end center=fix(num/2); scale=fix(num/10); a=center-scale; b=center+scale; disp ' pn(i)-fi(i) 的值为：' p_f(a:b)