Please give your large sparse matrix, we can talk about it. Because the types of sparse matrices are very huge, we can not answer you.

You may take any randomly sparse large matrix please. For your interest, using graph theory we have found determinant and use it to obtain numerical solution of linear sparse system. You may see research papers by R C Mittal and Ahmad al Kurdi.

To my knowledge, determinant is more of theoretical importance than numerical concern.  So could u show me your background where u have to compute the determinant of a matrix? Thanks.

Yes Zhang, you are right. I want to use it to find solution of linear or non-linear equations. We want to see other possibilities to find determinant. Thanks!