文档介绍：(1)Lagrange函数程序如下:
function yh = lagrange(x,y,xh)
n = length(x);m = length(xh);
x = reshape(x,n,1); y = reshape(y,n,1); xh = reshape(xh,m,1);
yh = zeros(m,1);c1 = ones(1,n-1);c2 = ones(m,1);
for i=1:n,
xp = x([1:i-1,i+1:n]);
yh = yh + y(i) * prod((xh*c1-c2*xp')./(c2*(x(i)*c1-xp')),2);
end
2 运行实验要求的程序
程序如下:
x=linspace(-1,1,13);y=1./(1+25.*x.^2);
x=linspace(-1,1,6);y=1./(1+25.*x.^2);
x1=linspace(-1,1,13);y1=lagrange(x,y,x1);
x=linspace(-1,1,11);y=1./(1+25.*x.^2);
x2=linspace(-1,1,13);y2=lagrange(x,y,x2);
x=linspace(-1,1,21);y=1./(1+25.*x.^2);
x3=linspace(-1,1,13);y3=lagrange(x,y,x3);
plot(x,y,'blue',x1,y1,'green',x2,y2,'red',x3,y3,'black')
3 标记纵坐标为“函数值”,横坐标为“x”,图像名字为“数值分析图像”,蓝色线为f(x),绿色线为L5(x),红色线为L10(x),黑色线为L20(x)。
实验数据:
x0=[0 3 5 7 9 11 12 13 14 15];
y0=[0 ];
x=0::15;
y1=lagrange(x0,y0,x); %前面编写的拉格朗日插值函数
y2=interp1(x0,y0,x);
y3=interp1(x0,y0,x,'spline');
pp1=csape(x0,y0);
y4=ppval(pp1,x);
pp2=csape(x0,y0,'seco