Eigenvalue VS Cholesky Decomposition

[brydustin]

Assuming the matrix is positive definite (necessary for cholesky decomposition).
Which is faster? Which is more accurate? Is there a reliable source that has all the most common decompositions listed in order of accuracy and speed?

 

[DuncanM]

What, exactly, is your question?

Are you asking the quickest way to check if a matrix is positive definite (either by calculating all the eigenvalues and checking that they are all greater than or equal to 0, or doing a Cholesky Decomposition)?

If so, doing the Cholesky Decomposition is the quickest and easiest way to check if a matrix is positive definite. Computing the eigenvalues is quite a task. The Cholesky Decomposition is a lot easier and faster; if the factorization succeeds, the matrix is positive definite. If the factorization fails, the matrix is not positive definite.