Algorithm 2.1: [MR.sup.3] for tsep: Compute selected eigenpairs of a symmetric tridiagonal T.
Note that we order the singular values ascendingly in order to simplify the transition between BSVD and TSEP.
There are two standard approaches to reduce the problem BSVD to TSEP, involving three different symmetric tridiagonal matrices.
Arguably the most straightforward approach to tackle the BSVD would be to just employ the [MR.sup.3]algorithm for TSEP (Algorithm 2.1) to compute eigendecompositions of BB*and B*B separately.
In contrast to TSEP, where it suffices to deal with the offdiagonal elements, now all entries of B are involved with the offdiagonals of [T.sub.GK](B), which makes preprocessing a bit more difficult.
Execute the [MR.sup.3]algorithm for TSEP (Algorithm 2.1), but take [M.sub.0]:= [T.sub.GK](B) as root representation in step 1, using the entries of B directly.