Is there a faster approach than \ operator to calculate the inverse of a lower triangular matrix?

Dear All,

I have a big square lower triangular matrix A (6000 x 6000) which is very sprase with a density 0.05%, I am using Inv_A=A\eye(size(A)) to calculate the inverse of A. But I found it still takes more than 3 seconds. I am wondering if there exists a faster approach to calculate the inverse of A.

Thanks.

Benson