  We propose a CJ-FEAST GSVDsolver to compute a partial generalized singular
value decomposition (GSVD) of a large matrix pair $(A,B)$ with the generalized
singular values in a given interval. The solver is a highly nontrivial
extension of the FEAST eigensolver for the (generalized) eigenvalue problem and
CJ-FEAST SVDsolver for the SVD problem. For a partial GSVD problem, given three
left and right searching subspaces, we propose a general projection method that
works on $(A,B)$ {\em directly}, and computes approximations to the desired
GSVD components. For the concerning GSVD problem, we exploit the
Chebyshev--Jackson (CJ) series to construct an approximate spectral projector
of the generalized eigenvalue problem of the matrix pair $(A^TA,B^TB)$
associated with the generalized singular values of interest, and use subspace
iteration on it to generate a right subspace. Premultiplying it with $A$ and
$B$ constructs two left subspaces. Applying the general projection method to
the subspaces constructed leads to the CJ-FEAST GSVDsolver. We derive accuracy
estimates for the approximate spectral projector and its eigenvalues, and
establish a number of convergence results on the underlying subspaces and the
approximate GSVD components obtained by the CJ-FEAST GSVDsolver. We propose
general-purpose choice strategies for the series degree and subspace dimension.
Numerical experiments illustrate the efficiency of the CJ-FEAST GSVDsolver.
