lagrange1.m

MatLab的拉格朗日插值法

% 分段线性Lagrange插值
% 命令格式：y=lagrange1(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=lagrange1(x0,y0,x)
[n1,n]=size(x0);[n1,m]=size(x);
for i=1:m
   u=x(i);
   if u<=x0(2)
      y(i)=y0(1)*(u-x0(2))/(x0(1)-x0(2))+...
         y0(2)*(u-x0(1))/(x0(2)-x0(1));
   elseif u>=x0(n-1)
      y(i)=y0(n-1)*(u-x0(n))/(x0(n-1)-x0(n))+...
         y0(n)*(u-x0(n-1))/(x0(n)-x0(n-1));
   else
      for k=2:n-1
         if u>=x0(k) & u<=x0(k+1)
            y(i)=y0(k)*(u-x0(k+1))/(x0(k)-x0(k+1))+...
               y0(k+1)*(u-x0(k))/(x0(k+1)-x0(k));
         end
      end
   end
end 
y;