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Several recent papers have introduced a periodic verification mechanism todetect silent errors in iterative solvers. Chen [PPoPP'13, pp. 167--176] hasshown how to combine such a verification mechanism (a stability test checkingthe orthogonality of two vectors and recomputing the residual) withcheckpointing: the idea is to verify every $d$ iterations, and to checkpointevery $c \times d$ iterations. When a silent error is detected by theverification mechanism, one can rollback to and re-execute from the lastcheckpoint. In this paper, we also propose to combine checkpointing andverification, but we use algorithm-based fault tolerance (ABFT) rather thanstability tests. ABFT can be used for error detection, but also for errordetection and correction, allowing a forward recovery (and no rollback norre-execution) when a single error is detected. We introduce an abstractperformance model to compute the performance of all schemes, and we instantiateit using the preconditioned conjugate gradient algorithm. Finally, we validateour new approach through a set of simulations.

A Backward/Forward Recovery Approach for the Preconditioned Conjugate Gradient Method