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We propose a CJ-FEAST GSVDsolver to compute a partial generalized singularvalue decomposition (GSVD) of a large matrix pair $(A,B)$ with the generalizedsingular values in a given interval. The solver is a highly nontrivialextension of the FEAST eigensolver for the (generalized) eigenvalue problem andCJ-FEAST SVDsolver for the SVD problem. For a partial GSVD problem, given threeleft and right searching subspaces, we propose a general projection method thatworks on $(A,B)$ {\em directly}, and computes approximations to the desiredGSVD components. For the concerning GSVD problem, we exploit theChebyshev--Jackson (CJ) series to construct an approximate spectral projectorof the generalized eigenvalue problem of the matrix pair $(A^TA,B^TB)$associated with the generalized singular values of interest, and use subspaceiteration on it to generate a right subspace. Premultiplying it with $A$ and$B$ constructs two left subspaces. Applying the general projection method tothe subspaces constructed leads to the CJ-FEAST GSVDsolver. We derive accuracyestimates for the approximate spectral projector and its eigenvalues, andestablish a number of convergence results on the underlying subspaces and theapproximate GSVD components obtained by the CJ-FEAST GSVDsolver. We proposegeneral-purpose choice strategies for the series degree and subspace dimension.Numerical experiments illustrate the efficiency of the CJ-FEAST GSVDsolver.

A CJ-FEAST GSVDsolver for computing a partial GSVD of a large matrix pair with the generalized singular values in a given interval