Suppose I have a symmetric positive definite matrix and I want to calculate all its eigenvalues and eigenvectors (eigenvalue decomposition). What's the most efficient algorithm (e.g. lowest complexity) to find that?
I found this question that shows a algorithm to find in $O(n^3 + (nlog^2 n) log b)$ for any matrix, since it doesn't take into account the fact that a matrix is symmetric and positive definite I suppose there is a faster algorithm for this case. I also found this paper, that has a method called "QR method" that works for symmetric real valued matrix, but it also doesn't take into account the positive definite.