Fast solution of dense linear system of fixed dimension (N=9), symmetric, positive-semidefinite

Question

Which algorithm you would recommend for fast solution of dense linear system of fixed dimension (N=9) (matrix is symmetric, positive-semidefinite)?

• Gaussian el

Answer 1

I would recommend LU decomposition, especially if "solved millions of times" really means "solved once and applied to millions of vectors". You'll create the LU decomposition, save it, and apply forward-back substitution against as many r.h.s. vectors as you wish.

It's more stable in the face of roundoff if you use pivoting.