You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Several recent papers have introduced a periodic verification mechanism to detect silent errors in iterative solvers. Chen [PPoPP'13, pp. 167--176] has shown how to combine such a verification mechanism (a stability test checking the orthogonality of two vectors and recomputing the residual) with checkpointing: the idea is to verify every @math iterations, and to checkpoint every @math iterations. When a silent error is detected by the verification mechanism, one can rollback to and re-execute from the last checkpoint. In this paper, we also propose to combine checkpointing and verification, but we use algorithm-based fault tolerance (ABFT) rather than stability tests. ABFT can be used for error detection, but also for error detection and correction, allowing a forward recovery (and no rollback nor re-execution) when a single error is detected. We introduce an abstract performance model to compute the performance of all schemes, and we instantiate it using the preconditioned conjugate gradient algorithm. Finally, we validate our new approach through a set of simulations.

Cited Abstract(s):
[1]: Main memory is one of the leading hardware causes for machine crashes in today's datacenters. Designing, evaluating and modeling systems that are resilient against memory errors requires a good understanding of the underlying characteristics of errors in DRAM in the field. While there have recently been a few first studies on DRAM errors in production systems, these have been too limited in either the size of the data set or the granularity of the data to conclusively answer many of the open questions on DRAM errors. Such questions include, for example, the prevalence of soft errors compared to hard errors, or the analysis of typical patterns of hard errors. In this paper, we study data on DRAM errors collected on a diverse range of production systems in total covering nearly 300 terabyte-years of main memory. As a first contribution, we provide a detailed analytical study of DRAM error characteristics, including both hard and soft errors. We find that a large fraction of DRAM errors in the field can be attributed to hard errors and we provide a detailed analytical study of their characteristics. As a second contribution, the paper uses the results from the measurement study to identify a number of promising directions for designing more resilient systems and evaluates the potential of different protection mechanisms in the light of realistic error patterns. One of our findings is that simple page retirement policies might be able to mask a large number of DRAM errors in production systems, while sacrificing only a negligible fraction of the total DRAM in the system.
Application-specific information can be very useful to enable ad-hoc solutions, which dramatically decrease the cost of detection. Many techniques have been advocated. They include memory scrubbing [1] and ABFT techniques (see below).