数值分析-龙格现象-matlab代码分享

龙格现象(Rungephenomenon)高次插值的病态性质1.先建立一个n+1个插值节点的拉格朗日插值多项式functionlangrange=langrange(x,n)langrange=0;xx=linspace(-5,5,n+1);fori=1:n+1lix=1;forj=1:n+1ifj~=ilix=lix.*((x-xx(j))./(xx(i)-xx(j)));endendlangrange=fun(xx(i)).*lix+langrange;endend2.再建立一个龙格函数functionf=fun(x)f=1./(1+x.^2);3.在同一坐标系中画出龙格函数和拉格朗日插值多项式的图像functionrunge_phen(n)%n为Lagrange插值节点的个数x=linspace(-5,5,100);plot(x,fun(x),'r+',x,langrange(x,n),'b*');4.在Matlab命令窗口运行如下命令runge_phen(10)