smallest and largest eigenvalue of discretized operator $-d^2/dx^2$

116 Views Asked by At

In 1D, the second order derivative operator $-d^2/dx^2$ can be discretized as, using Matlab

n = 501; h = 1/(n-1);
A = 1/h*spdiags(ones(n,1)*[-1 2 -1],-1:1,n,n); 
[V,D]=eig(full(A));

Now I am wondering about what information do the smallest(0.0196) and largest(2000) eigenvalues give?

how is it related to the discretization?