A band-Lanczos generalization of bidiagonal decomposition

In a seminal paper from 1965 Golub and Kahan gave two different but mathematical equivalent algorithms for computing the bidiagonal decomposition $A = UBV^T$ of a general matrix. The first algorithm uses Householder transformations applied alternately from left and right to $A$. The second uses a coupled two-term recurrence relation related to the symmetric Lanczos process. The latter is used, for example, in LSQR to compute a partial bidiagonal decomposition for large scale linear least squares problems.

Recently Paige and Strakos have shown that reduction to upper bidiagonal form of the augmented matrix $(b,\,A)$ provides a minimally dimensioned generic core problem for scaled total least squares problems. Using ideas from Ruhe 1979 we develop a band-Lanczos algorithm that generalizes the bidiagonal decomposition This provides a natural extension of results of Paige and Strakos to the case of multiple right hand sides.