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% lagrange.m

function y=lagrange(x0,y0,x)
%  inputs:
%         x0:系数矩阵，维度为n*1
%         y0:载荷矩阵，维度为n*1
%         x:绘图点矩阵，维度为m*1
%  outputs:
%         y:未知量矩阵，维度m*1
n=length(x0);
m=length(x);
for i1=1:m
    temp=x(i1);
    sum=0;
    for i2=1:n
        l=1;
        for i3=1:n
            if i2~=i3
                l=l*(temp-x0(i3))/(x0(i2)-x0(i3));
            end
        end
        sum=sum+l*y0(i2);
    end
    y(i1)=sum;
end
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% assignment1.m

clear;
x=-1:0.001:1;
y=1./(1+25.*x.*x);
x1=-1:2/4:1;
y1=1./(1+25.*x1.*x1);
x2=-1:2/10:1;
y2=1./(1+25.*x2.*x2);
plot(x,y,'b');
hold on;
y=lagrange(x1,y1,x);
plot(x,y,'r');
hold on;
y=lagrange(x2,y2,x);
plot(x,y,'g');