  The FEAST eigensolver is extended to the computation of the singular triplets
of a large matrix $A$ with the singular values in a given interval. The
resulting FEAST SVDsolver is subspace iteration applied to an approximate
spectral projector of $A^TA$ corresponding to the desired singular values in a
given interval, and constructs approximate left and right singular subspaces
corresponding to the desired singular values, onto which $A$ is projected to
obtain Ritz approximations. Differently from a commonly used contour
integral-based FEAST solver, we propose a robust alternative that constructs
approximate spectral projectors by using the Chebyshev--Jackson polynomial
series, which are symmetric positive semi-definite with the eigenvalues in
$[0,1]$. We prove the pointwise convergence of this series and give compact
estimates for pointwise errors of it and the step function that corresponds to
the exact spectral projector. We present error bounds for the approximate
spectral projector and reliable estimates for the number of desired singular
triplets, establish numerous convergence results on the resulting FEAST
SVDsolver, and propose practical selection strategies for determining the
series degree and for reliably determining the subspace dimension. The solver
and results on it are directly applicable or adaptable to the real symmetric
and complex Hermitian eigenvalue problem. Numerical experiments illustrate that
our FEAST SVDsolver is at least competitive with and is much more efficient
than the contour integral-based FEAST SVDsolver when the desired singular
values are extreme and interior ones, respectively, and it is also more robust
than the latter.
