Lagrange插值MATLAB源程序

1、%lagrange插值多项式Lagrange插值MATLAB源程序functiony=lagrange(xO,yO,x);% x0自变量取值向量已知 yO为已知对应x0的函数取值，x为要求插值点坐标n=len gth(x0);m=le ngth(x);for i=1:mz=x(i);s=0.0;for k=1: np=1.0;for j=1: nif j=kp=p*(z-x0(j)/(x0(k)-x0(j);%插值基函数endends=p*y0(k)+s;endy(i)=s;end测试：x0=0:2y0=2 3 5x=0.5Lagra nge(x0,y0,x)x0=0:2 y0=2 3 5 x

2、=0:0.01:2Lagra nge(x0,y0,x)Newton插值MATLA源程序fun cti onf=Newt on( x,y,xO)syms t ;n = len gth(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

3、 = collect(f);endendendtest:x=1 -1 2 y=0 -3 4 x0=-1:0.1:2Newt on (x,y,xO)分段插值MATLA源程序fun cti ony = div_li near(xO,yO,x, n)for i = 1:n-1if (x = x0(i) & (x =jt(i,j)=(t(i,j-1)-t(i-1,j-1)/(x(i)-x(i-j+1);endendendfor k=1:ns=1;m=1;for j=1:kif jnewtonNewton插值 MATLAB!程序fun cti onyi=n ewt on( x,y,xi)m=length

4、(x);n=length(y);); endif m=n error( x and y must same f=zeros(n+1,1);k=2;f(1)=y(1)while k=n+1f(1)=y(k);k,x(k)for i=1:k-1if i=k-1 f(i+1)=(f(i)-y(i)/(x(k)-x(i);endendcs(i)=f(i+1); y(k)=f(k);k=k+1;endcfwh=0;for i=1:n-2w=1;for j=1:i w=w*(xi-x(j);endcfwh=cfwh+cs(i)*w;endyi=y(1)+cfwh;x=0:2y=2 3 5xi=0.5new

5、ton(x,y,xi)Newton2)function f = Newton(x,y,x0)syms t;if(length(x) = length(y)n = length(x);c(1:n) = 0.0;elsedisp(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 = y1;if(i=n-1) if(nargin

6、 = 3) f = subs(f,t,x0);elsef = collect(f);式展% 将 插 值 多 项 开 f = vpa(f, 6);endendend x=0:2y=2 3 5x0=0.5Newton(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;for i=1:n t(i,1)=y(i);endfor j=2:nfor i=2:nif i=j t(i,j)=(t(i,j-1)-t(i-1,j-1)/(x(i)-x(i- j+1);endendendfor k=1:n s=1;m=1;for j=1:k if jk s=s*(v-x(j); end endm=s*t(k,k); u=u+m; end disp( 插