  The cross-product matrix-based CJ-FEAST SVDsolver proposed previously by the
authors is shown to compute the left singular vector possibly much less
accurately than the right singular vector and may be numerically backward
unstable when a desired singular value is small. In this paper, an alternative
augmented matrix-based CJ-FEAST SVDsolver is considered to compute the singular
triplets of a large matrix $A$ with the singular values in an interval $[a,b]$
contained in the singular spectrum. The new CJ-FEAST SVDsolver is a subspace
iteration applied to an approximate spectral projector of the augmented matrix
$[0, A^T; A, 0]$ associated with the eigenvalues in $[a,b]$, and constructs
approximate left and right singular subspaces with the desired singular values
independently, onto which $A$ is projected to obtain the Ritz approximations to
the desired singular triplets. Compact estimates are given for the accuracy of
the approximate spectral projector, and a number of convergence results are
established. The new solver is proved to be always numerically backward stable.
A convergence comparison of the cross-product and augmented matrix-based
CJ-FEAST SVDsolvers is made, and a general-purpose choice strategy between the
two solvers is proposed for the robustness and overall efficiency. Numerical
experiments confirm all the results.
