  As we stride toward the exascale era, due to increasing complexity of
supercomputers, hard and soft errors are causing more and more problems in
high-performance scientific and engineering computation. In order to improve
reliability (increase the mean time to failure) of computing systems, a lot of
efforts have been devoted to developing techniques to forecast, prevent, and
recover from errors at different levels, including architecture, application,
and algorithm. In this paper, we focus on algorithmic error resilient iterative
linear solvers and introduce a redundant subspace correction method. Using a
general framework of redundant subspace corrections, we construct iterative
methods, which have the following properties: (1) Maintain convergence when
error occurs assuming it is detectable; (2) Introduce low computational
overhead when no error occurs; (3) Require only small amount of local
(point-to-point) communication compared to traditional methods and maintain
good load balance; (4) Improve the mean time to failure. With the proposed
method, we can improve reliability of many scientific and engineering
applications. Preliminary numerical experiments demonstrate the efficiency and
effectiveness of the new subspace correction method.
