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The cross-product matrix-based CJ-FEAST SVDsolver proposed previously by theauthors is shown to compute the left singular vector possibly much lessaccurately than the right singular vector and may be numerically backwardunstable when a desired singular value is small. In this paper, an alternativeaugmented matrix-based CJ-FEAST SVDsolver is considered to compute the singulartriplets 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 subspaceiteration applied to an approximate spectral projector of the augmented matrix$[0, A^T; A, 0]$ associated with the eigenvalues in $[a,b]$, and constructsapproximate left and right singular subspaces with the desired singular valuesindependently, onto which $A$ is projected to obtain the Ritz approximations tothe desired singular triplets. Compact estimates are given for the accuracy ofthe approximate spectral projector, and a number of convergence results areestablished. The new solver is proved to be always numerically backward stable.A convergence comparison of the cross-product and augmented matrix-basedCJ-FEAST SVDsolvers is made, and a general-purpose choice strategy between thetwo solvers is proposed for the robustness and overall efficiency. Numericalexperiments confirm all the results.

An augmented matrix-based CJ-FEAST SVDsolver for computing a partial singular value decomposition with the singular values in a given interval