  Lanczos-type algorithms are well known for their inherent instability. They
typically breakdown when relevant orthogonal polynomials do not exist. Current
approaches to avoiding breakdown rely on jumping over the non-existent
polynomials to resume computation. This jumping strategy may have to be used
many times during the solution process. We suggest an alternative to jumping
which consists in switching between different algorithms that have been
generated using different recurrence relations between orthogonal polynomials.
This approach can be implemented as three different strategies: ST1, ST2, and
ST3. We shall briefly recall how Lanczos-type algorithms are derived. Four of
the most prominent such algorithms namely $A_4$, $A_{12}$, $A_5/B_{10}$ and
$A_5/B_8$ will be presented and then deployed in the switching framework. In
this paper, only strategy ST2 will be investigated. Numerical results will be
presented.
