Resilient matrix multiplication of hierarchical semi-separable matrices

Abstract

The hierarchical semi-separable (HSS) matrix factorization has useful characteristics for representing low-rank operators on extreme scale computing systems. To prepare for the higher error rates anticipated with future architectures, this paper introduces new faulttolerant algorithms for HSS matrix multiplication that maintain efficient performance in the presence of high error rates. The measured runtime overhead for error checking and data preservation using the Containment Domains library is exceptionally small and encourages the use of frequent, fine-grained error checking when using algorithm based fault tolerance.