# What is the fastest algorithm for computing log determinant of a PSD matrix? (All possible PSD matrices)

I am diving into some literature to understand which is the best algorithm for computing the log-determinant of a PSD matrix. More generally, I am interested in a list of resources to read, which cover all the possible cases of matrix (i.e. sparse, dense, low rank, etc..) with all the probability of failure and error (relative, absolute, etc..).

So far I have found the following two papers:

We were just wondering if there are other algorithms with better asymptotics, different techniques, or other paper that we should be aware of.

Similar question on Computational Science are:

• How large are the matrices of interest? Are they sparse or dense? – Brian Borchers Dec 2 '19 at 13:06
• How accurate do you need the result to be? In particular, do you want the runtime to scale logarithmically with the precision or can you handle polynomial dependence on the estimate precision? – cdipaolo Dec 3 '19 at 0:13
• Hi, I edited the question to specify that I am interested in all of these cases. – asdf Dec 16 '19 at 21:50