  In this paper, we derive new model formulations for computing generalized
singular values of a Grassman matrix pair. These new formulations make use of
truncated filter matrices to locate the $i$-th generalized singular value of a
Grassman matrix pair. The resulting matrix optimization problems can be solved
by using numerical methods involving Newton's method on Grassmann manifold.
Numerical examples on synthetic data sets and gene expression data sets are
reported to demonstrate the high accuracy and the fast computation of the
proposed new ormulations for computing arbitrary generalized singular value of
Grassman matrix pair.
