Soft error vulnerability of iterative linear algebra methods

Devices are increasingly vulnerable to soft errors as their feature sizes shrink. Previously, soft error rates were significant primarily in space and high-atmospheric computing. Modern architectures now use features so small at sufficiently low voltages that soft errors are becoming important even at terrestrial altitudes. Due to their large number of components, supercomputers are particularly susceptible to soft errors. Since many large scale parallel scientific applications use iterative linear algebra methods, the soft error vulnerability of these methods constitutes a large fraction of the applications' overall vulnerability. Many users consider these methods invulnerable to most soft errors since they converge from an imprecise solution to a precise one. However, we show in this paper that iterative methods are vulnerable to soft errors, exhibiting both silent data corruptions and poor ability to detect errors. Further, we evaluate a variety of soft error detection and tolerance techniques, including checkpointing, linear matrix encodings, and residual tracking techniques.