positive-definiteness of a huge sparse matrix

I want to determine the positive-definiteness of a huge sparse matrix (N^2,N^2) with nonzeros on the 9 off-diagnols, where N is the larger the better. I am using eigs(A,1,'SA') because of the memory issues, however, for N=260, each iteraction requires 1 hour. I really want to find out fast method to deal this problem.

Answer 1

[Sean de Wolski]

http://www.mathworks.com/support/solutions/en/data/1-WQKKX/index.html

Answer 2

[Andrew Knyazev]

try http://www.mathworks.com/matlabcentral/fileexchange/48-lobpcg-m