For a stationary set S ⊆ ω1 and a ladder system C over S, a new type of gaps called C-Hausdorff is introduced and investigated. We describe a forcing model of ZFC in which, for some stationary set S, for every ladder C over S, every gap contains a subgap that is CHausdorff. But for every ladder E over ω1 \ S there exists a gap with no subgap that is E-Hausdorff. A new type of chain condition, c...

Compared to the classical Lanczos algorithm, s-step variant has potential improve performance by asymptotically decreasing synchronization cost per iteration. However, this comes at a price; despite being mathematically equivalent, may behave quite differently in finite precision, potentially exhibiting greater loss of accuracy and slower convergence relative algorithm. It previously been shown...