I have some code (given to me) that that uses DGETRF for computing an LU factorization of a general M*N matrix A. Then I use DGETRI to compute the inverse of A.

The problem is that A is huge, making this operation the bottleneck of the program. For that reason, I am looking for alterntives, in order to do better. I see that A matrix is symmetric positive definite (SPD) and not a general matrix, so could I take advantage of this property somehow?

For example, I saw a function that performs Cholesky factorization of a SPD matrix. However, I did not find any such function for LU. Is there any?

Now, I am refreshing my linear algebra knowledge on whether I can discard LU and go for Cholesky.