lagrange2.m

MatLab的拉格朗日插值法

% 分段二次Lagrange插值
% 命令格式：y=lagrange2(x0,y0,x)
% x0为节点向量，y0为对应的函数值向量，
% x为插值点向量，返回值y为x处的函数近似值向量。
function y=lagrange2(x0,y0,x)
n=length(x0);
m=length(x);
for i=1:m
   u=x(i);
   if u<=x0(2)
      y(i)=y0(1)*(u-x0(2))*(u-x0(3))/(x0(1)-x0(2))/(x0(1)-x0(3))+...
         y0(2)*(u-x0(1))*(u-x0(3))/(x0(2)-x0(1))/(x0(2)-x0(3))+...
         y0(3)*(u-x0(1))*(u-x0(2))/(x0(3)-x0(1))/(x0(3)-x0(2));
   elseif x(i)>x0(n-1)
      y(i)=y0(n-2)*(u-x0(n-1))*(u-x0(n))/(x0(n-2)-x0(n-1))/(x0(n-2)-x0(n))+...
         y0(n-1)*(u-x0(n-2))*(u-x0(n))/(x0(n-1)-x0(n-2))/(x0(n-1)-x0(n))+...
         y0(n)*(u-x0(n-1))*(u-x0(n-2))/(x0(n)-x0(n-1))/(x0(n)-x0(n-2));
   else
      for k=2:n-1
         if u>(x0(k)+x0(k-1))/2 & u<=(x0(k)+x0(k+1))/2
            y(i)=y0(k-1)*(u-x0(k))*(u-x0(k+1))/(x0(k-1)-x0(k))/(x0(k-1)-x0(k+1))+...
               y0(k)*(u-x0(k-1))*(u-x0(k+1))/(x0(k)-x0(k-1))/(x0(k)-x0(k+1))+...
               y0(k+1)*(u-x0(k-1))*(u-x0(k))/(x0(k+1)-x0(k-1))/(x0(k+1)-x0(k));
         end
      end
   end
end
y;