The Look-ahead Lanczos Bi-orthogonalization process is a generalization of the Lanczos bi-orthoganilization (as used in, for instance, QMR) [^Freund1993], [^Freund1994]. The look-ahead process detects (near-)singularities during the construction of the Lanczos iterates, known as break-down, and skips over them. This is particularly advantageous for linear systems with large null-spaces or eigenvalues close to 0.
We provide an iterator interface for the Lanczos decomposition (Freund, 1994), where the look-ahead Lanczos process is implemented as a two-term coupled recurrence.
IterativeSolvers.LookAheadLanczosDecomp
IterativeSolvers.LookAheadLanczosDecompLog