数值分析第二次大作业1（1）用 Lagrange 插值法程序：function f=Lang(x,y,x0)syms t;f=0;n=length(x);for(i=1:n) l=y(i); for(j=1:i-1) l=l*(t-x(j))/(x(i)-x(j)); end; for(j=i+1:n) l=l*(t-x(j))/(x(i)-x(j)); end f=f+l; simplify(f); if(i==n) if(nargin==3) f=subs(f,'t',x0); else f=collect(f); f=vpa(f,6); end endendx=[1,2,3,-4,5];y=[2,48,272,1182,2262];t=[-1];disp('插值成果')yt=Lang(x,y,t)disp('插值多项式')yt=Lang(x,y)ezplot(yt,[-1,5]);运行成果：插值成果：Yt= 12.0000插值多项式：yt =4.0*t^4 - 2.0*t^3 + t^2 - 3.0*t + 2.0（2）构造 arctan x 在[1,6]基于等距节点旳 10 次插值多项式程序：function f=New(x,y,x0)syms t;if(length(x)==length(y)) n=length(x); c(1:n)=0.0;else disp('xºÍyάÊý²»µÈ£¡'); return;endf=y(1);y1=0;xx=linspace(x(1),x(n),(x(2)-x(1)));for(i=1:n-1) for(j=1:n-i) y1(j)=y(j+1)-y(j); end c(i)=y1(1); l=t; for(k=1:i-1) l=l*(t-k); end; f=f+c(i)*l/factorial(i); simplify(f); y=y1; if(i==n-1) if(nargin==3) f=subs(f,'t',(x0-x(1))/(x(2)-x(1))); else f=collect(f); f=vpa(f,6); end endend>> x=[1,1.5,2,2.5,3,3.5,4,4.5,5,5.5,6];y=[atan(1),atan(1.5),atan(2),atan(2.5),atan(3),atan(3.5),atan(4),atan(4.5),atan(5),atan(5.5),atan(6)];disp('插值多项式')yt=New(x,y)ezplot(yt,[1,6]);hold onezplot('atan(t)',[1,6])grid on运行成果：插值多项式yt =1.34684*10^(-10)*t^10 - 6.61748*10^(-9)*t^9 + 1.28344*10^(-7)*t^8 - 0.*t^7 - 0.*t^6 + 0.*t^5 - 0.00176296*t^4 + 0.0125826*t^3 - 0.0640379*t^2 + 0.250468*t + 0.7853982（1）用 MATLAB 自带 spline 函数用于进行三次样条插值程序：>> x=[-5,-4,-3,-2,-1,0,1,2,3,4,5];y=[0.03846,0.05882,0.10000,0.0,0.50000,1.00000,0.50000,0.0,0.10000,0.05882,0.03846];xi=linspace(-5,5)yi=spline(x,y,xi);plot(x,y,'rp',xi,yi);hold on;syms xfx=1/(1+x^2);ezplot(fx);grid on运行成果：由图可知，三次样条插值多项式图像与原函数图像基本一致。（2）取第一类边界条件，用三弯矩法编写 MATLAB 程序程序 function yi=cubic_spline(x,y,ydot,xi)n=length(x);ny=length(y);h=zeros(1,n);lambda=ones(1,n);mu=ones(1...
