PSVDPartial Singular Value Decomposition
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When using an implicitly restarted GK bidiagonalization to solve for a PSVD of A, a heuristic was proposed in [26] to require that the relative gap between the approximating value [[??].sup.2.sub.k] and all shifts [[??].sub.i], defined by
As the matrices whose SVD have to be computed are of order m + n and rank m + n - 1, and we are only interested in computing the right singular vector associated to its smallest singular value, we can consider, for computing this SVD, the partial singular value decomposition algorithm (PSVD) described in [22] and [23], and whose FORTRAN code is available in netlih (see
The partial singular value decomposition algorithm (PSVD) presented in [22] and [23] is specially suitable in our case because only the smallest singular value and its associated right singular vector are required, and the gap between the singular values associated to the desired and undesired singular vectors is large.