Lagrange插值MATLAB源程序

1、Lagrange#值MATLAB源程序functiony=lagrange(x0,y0,x);取值，x为要求插值点坐标n=length(x0);m=length(x);fori=1:mz=x(i);s=0.0;fork=1:np=1.0;forj=1:nifj=kp=p*(z-x0(j)/(x0(k)-x0(j);%x0自变量取值向量y0为对应x0的函数%插值基函数endends=p*y0(k)+s;endy(i)=s;end测试：x0=0:2y0=235Lagrange(x0,y0,x)%lagrange插值多项式x0=0:2y0=235x=:2Lagrange(x0,y0,x)Newton

2、插值MATLAB程序functionf=Newton(x,y,x0)symst;n=length(x);c(1:n)=0.0;f=y(1);y1=0;l=1;for(i=1:n-1)for(j=i+1:n)y1(j)=(y(j)-y(i)/(x(j)-x(i);endc(i)=y1(i+1);l=l*(t-x(i);f=f+c(i)*l;simplify(f);y=yi;if(i=n-1)if(nargin=3)f=subs(f,t,x0);elsef=collect(f);endendendtest:x=1-12y=0-34x0=-1:0.1:2Newton(x,y,x0)分段插值MATLA

3、B源程序functiony=div_linear(x0,y0,x,n)fori=1:n-1-x0(i+1)*y0(i)+(xx0(i)/(x0(i+1)if(x=x0(i)&(x=jt(i,j)=(t(i,j-1)-t(i-1,j-1)/(x(i)-x(i-j+1);endendendfork=1:ns=1;m=1;forj=1:kifjnewtonNewton插值MATLAB源程序functionyi=newton(x,y,xi)m=length(x);n=length(y);ifm=nerror(xandymustsame);endf=zeros(n+1,1);k=2;f(1)=y(1)w

4、hilek=n+1f(1)=y(k);k,x(k)fori=1:k-1ifi=k-1f(i+1)=(f(i)-y(i)/(x(k)-x(i);endendcs(i)=f(i+1);y(k)=f(k);k=k+1;endcfwh=0;fori=1:n-2w=1;forj=1:iw=w*(xi-x(j);endcfwh=cfwh+cs(i)*w;endyi=y(1)+cfwh;x=0:2y=235xi=newton(x,y,xi)Newton2)functionf=Newton(x,y,x0)symst;if(length(x)=length(y)n=length(x);c(1:n)=0.0;el

5、sedisp(x和y的维数不相等！);return;endf=y(1);y1=0;l=1;for(i=1:n-1)for(j=i+1:n)y1(j)=(y(j)-y(i)/(x(j)-x(i);endc(i)=y1(i+1);l=l*(t-x(i);f=f+c(i)*l;simplify(f);y=yi;if(i=n-1)if(nargin=3)f=subs(f,t,x0);elsef=vpa(f,6);f=collect(f);福插值多项式展开endendendx=0:2y=235x0Newton(x,y,x0)function=Newton(x,y,v)x=input(X数组=:);y=input(Y数组=:);v=input(插值点数值=:);n=length(x);t=zeros(n,n);u=0;fori=1:nt(i,1)=y(i)；endforj=2:nfori=2:nifi=jt(i,j)=(t(i,j-1)-t(i-1,j-1)/(x(i)-x(i-j+1);endendendfork=1:ns=1;m=1;forj=1:kifjks=s*(v-x(j);endendm=s*t(k,k);u=u+m;e