I have a tridiagonal matrix (1000×1000) with each element equal to $1$ except {n, n} = 2
. It takes 8 hours to give me the eigenvalues?!!
Here is the code I used:
n=1000;
m = SparseArray[{Band[{1, 2}] -> 1, Band[{2, 1}] -> 1,
Band[{2, 2}, {n - 1, n - 1}] -> 2 , {1, 1} -> 2, {n, n} ->
2 , {1, n} -> 0, {n, 1} -> 0}, {n, n}];
N[Eigenvalues[m]];
m//MatrixForm
$\endgroup$...consider using N on the matrix ...
$\endgroup$