How expensive is it to compute the eigenvalues of a matrix?
What is the complexity of the best algorithms?
How long might it take in practice if I have a 1000x1000 matrix? I assume it helps if the matrix is sparse?
Are there any cases where the eigenvalue computation would not terminate?
In R
, I can compute the eigenvalues as in the following toy example:
> m<-matrix( c(13,2, 5,4), ncol=2, nrow=2 )
> eigen(m, only.values=1)
$values
[1] 14 3
Does anyone know what algorithm it uses?
Are there any other (open-source) packages that compute the eigenvalue?